[{"day":"01","publisher":"American Institute of Physics","date_published":"2012-01-01T00:00:00Z","publication":"Journal of Mathematical Physics","abstract":[{"lang":"eng","text":"We study the BCS gap equation for a Fermi gas with unequal population of spin-up and spin-down states. For cosh (δ μ/T) ≤ 2, with T the temperature and δμ the chemical potential difference, the question of existence of non-trivial solutions can be reduced to spectral properties of a linear operator, similar to the unpolarized case studied previously in [Frank, R. L., Hainzl, C., Naboko, S., and Seiringer, R., J., Geom. Anal.17, 559-567 (2007)10.1007/BF02937429; Hainzl, C., Hamza, E., Seiringer, R., and Solovej, J. P., Commun., Math. Phys.281, 349-367 (2008)10.1007/s00220-008-0489-2; and Hainzl, C. and Seiringer, R., Phys. Rev. B77, 184517-110 435 (2008)]10.1103/PhysRevB.77.184517. For cosh (δ μ/T) &gt; 2 the phase diagram is more complicated, however. We derive upper and lower bounds for the critical temperature, and study their behavior in the small coupling limit."}],"publist_id":"4532","doi":"10.1063/1.3670747","publication_status":"published","date_created":"2018-12-11T11:57:25Z","volume":53,"status":"public","quality_controlled":0,"author":[{"last_name":"Freiji","first_name":"Abraham","full_name":"Freiji, Abraham"},{"last_name":"Hainzl","first_name":"Christian","full_name":"Hainzl, Christian"},{"orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"citation":{"ieee":"A. Freiji, C. Hainzl, and R. Seiringer, “The gap equation for spin-polarized fermions,” <i>Journal of Mathematical Physics</i>, vol. 53, no. 1. American Institute of Physics, 2012.","ista":"Freiji A, Hainzl C, Seiringer R. 2012. The gap equation for spin-polarized fermions. Journal of Mathematical Physics. 53(1).","short":"A. Freiji, C. Hainzl, R. Seiringer, Journal of Mathematical Physics 53 (2012).","mla":"Freiji, Abraham, et al. “The Gap Equation for Spin-Polarized Fermions.” <i>Journal of Mathematical Physics</i>, vol. 53, no. 1, American Institute of Physics, 2012, doi:<a href=\"https://doi.org/10.1063/1.3670747\">10.1063/1.3670747</a>.","ama":"Freiji A, Hainzl C, Seiringer R. The gap equation for spin-polarized fermions. <i>Journal of Mathematical Physics</i>. 2012;53(1). doi:<a href=\"https://doi.org/10.1063/1.3670747\">10.1063/1.3670747</a>","apa":"Freiji, A., Hainzl, C., &#38; Seiringer, R. (2012). The gap equation for spin-polarized fermions. <i>Journal of Mathematical Physics</i>. American Institute of Physics. <a href=\"https://doi.org/10.1063/1.3670747\">https://doi.org/10.1063/1.3670747</a>","chicago":"Freiji, Abraham, Christian Hainzl, and Robert Seiringer. “The Gap Equation for Spin-Polarized Fermions.” <i>Journal of Mathematical Physics</i>. American Institute of Physics, 2012. <a href=\"https://doi.org/10.1063/1.3670747\">https://doi.org/10.1063/1.3670747</a>."},"extern":1,"issue":"1","year":"2012","intvolume":"        53","month":"01","date_updated":"2021-01-12T06:57:13Z","type":"journal_article","_id":"2394","title":"The gap equation for spin-polarized fermions"},{"main_file_link":[{"url":"http://arxiv.org/abs/1102.4001","open_access":"1"}],"title":"Microscopic derivation of Ginzburg-Landau theory","date_updated":"2021-01-12T06:57:13Z","_id":"2395","type":"journal_article","year":"2012","intvolume":"        25","month":"01","page":"667 - 713","oa":1,"issue":"3","author":[{"last_name":"Frank","full_name":"Frank, Rupert L","first_name":"Rupert"},{"full_name":"Hainzl, Christian","first_name":"Christian","last_name":"Hainzl"},{"orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Robert Seiringer","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Solovej","full_name":"Solovej, Jan P","first_name":"Jan"}],"quality_controlled":0,"status":"public","extern":1,"citation":{"ieee":"R. Frank, C. Hainzl, R. Seiringer, and J. Solovej, “Microscopic derivation of Ginzburg-Landau theory,” <i>Journal of the American Mathematical Society</i>, vol. 25, no. 3. American Mathematical Society, pp. 667–713, 2012.","ista":"Frank R, Hainzl C, Seiringer R, Solovej J. 2012. Microscopic derivation of Ginzburg-Landau theory. Journal of the American Mathematical Society. 25(3), 667–713.","mla":"Frank, Rupert, et al. “Microscopic Derivation of Ginzburg-Landau Theory.” <i>Journal of the American Mathematical Society</i>, vol. 25, no. 3, American Mathematical Society, 2012, pp. 667–713, doi:<a href=\"https://doi.org/10.1090/S0894-0347-2012-00735-8\">10.1090/S0894-0347-2012-00735-8</a>.","short":"R. Frank, C. Hainzl, R. Seiringer, J. Solovej, Journal of the American Mathematical Society 25 (2012) 667–713.","ama":"Frank R, Hainzl C, Seiringer R, Solovej J. Microscopic derivation of Ginzburg-Landau theory. <i>Journal of the American Mathematical Society</i>. 2012;25(3):667-713. doi:<a href=\"https://doi.org/10.1090/S0894-0347-2012-00735-8\">10.1090/S0894-0347-2012-00735-8</a>","chicago":"Frank, Rupert, Christian Hainzl, Robert Seiringer, and Jan Solovej. “Microscopic Derivation of Ginzburg-Landau Theory.” <i>Journal of the American Mathematical Society</i>. American Mathematical Society, 2012. <a href=\"https://doi.org/10.1090/S0894-0347-2012-00735-8\">https://doi.org/10.1090/S0894-0347-2012-00735-8</a>.","apa":"Frank, R., Hainzl, C., Seiringer, R., &#38; Solovej, J. (2012). Microscopic derivation of Ginzburg-Landau theory. <i>Journal of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/S0894-0347-2012-00735-8\">https://doi.org/10.1090/S0894-0347-2012-00735-8</a>"},"doi":"10.1090/S0894-0347-2012-00735-8","publication_status":"published","date_created":"2018-12-11T11:57:25Z","volume":25,"abstract":[{"text":"We give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit is semiclassical in nature, and semiclassical analysis, with minimal regularity assumptions, plays an important part in our proof. ","lang":"eng"}],"publist_id":"4531","publisher":"American Mathematical Society","day":"01","date_published":"2012-01-01T00:00:00Z","publication":"Journal of the American Mathematical Society"},{"author":[{"last_name":"Landon","first_name":"Benjamin","full_name":"Landon, Benjamin"},{"last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Robert Seiringer"}],"quality_controlled":0,"status":"public","citation":{"mla":"Landon, Benjamin, and Robert Seiringer. “The Scattering Length at Positive Temperature.” <i>Letters in Mathematical Physics</i>, vol. 100, no. 3, Springer, 2012, pp. 237–43, doi:<a href=\"https://doi.org/10.1007/s11005-012-0566-5\">10.1007/s11005-012-0566-5</a>.","short":"B. Landon, R. Seiringer, Letters in Mathematical Physics 100 (2012) 237–243.","ieee":"B. Landon and R. Seiringer, “The scattering length at positive temperature,” <i>Letters in Mathematical Physics</i>, vol. 100, no. 3. Springer, pp. 237–243, 2012.","ista":"Landon B, Seiringer R. 2012. The scattering length at positive temperature. Letters in Mathematical Physics. 100(3), 237–243.","apa":"Landon, B., &#38; Seiringer, R. (2012). The scattering length at positive temperature. <i>Letters in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s11005-012-0566-5\">https://doi.org/10.1007/s11005-012-0566-5</a>","chicago":"Landon, Benjamin, and Robert Seiringer. “The Scattering Length at Positive Temperature.” <i>Letters in Mathematical Physics</i>. Springer, 2012. <a href=\"https://doi.org/10.1007/s11005-012-0566-5\">https://doi.org/10.1007/s11005-012-0566-5</a>.","ama":"Landon B, Seiringer R. The scattering length at positive temperature. <i>Letters in Mathematical Physics</i>. 2012;100(3):237-243. doi:<a href=\"https://doi.org/10.1007/s11005-012-0566-5\">10.1007/s11005-012-0566-5</a>"},"extern":1,"doi":"10.1007/s11005-012-0566-5","date_created":"2018-12-11T11:57:25Z","publication_status":"published","volume":100,"abstract":[{"lang":"eng","text":"A positive temperature analogue of the scattering length of a potential V can be defined via integrating the difference of the heat kernels of -Δ and, with Δ the Laplacian. An upper bound on this quantity is a crucial input in the derivation of a bound on the critical temperature of a dilute Bose gas (Seiringer and Ueltschi in Phys Rev B 80:014502, 2009). In (Seiringer and Ueltschi in Phys Rev B 80:014502, 2009), a bound was given in the case of finite range potentials and sufficiently low temperature. In this paper, we improve the bound and extend it to potentials of infinite range."}],"publist_id":"4529","publisher":"Springer","day":"01","date_published":"2012-06-01T00:00:00Z","publication":"Letters in Mathematical Physics","main_file_link":[{"url":"http://arxiv.org/abs/1111.1683","open_access":"1"}],"title":"The scattering length at positive temperature","date_updated":"2021-01-12T06:57:13Z","_id":"2396","type":"journal_article","intvolume":"       100","year":"2012","month":"06","page":"237 - 243","oa":1,"issue":"3"},{"main_file_link":[{"url":"http://arxiv.org/abs/1105.1100","open_access":"1"}],"title":"Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs","date_updated":"2021-01-12T06:57:14Z","type":"journal_article","_id":"2397","intvolume":"       100","year":"2012","month":"05","page":"119 - 138","oa":1,"issue":"2","quality_controlled":0,"author":[{"first_name":"Christian","full_name":"Hainzl, Christian","last_name":"Hainzl"},{"first_name":"Robert","full_name":"Robert Seiringer","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer"}],"status":"public","citation":{"ama":"Hainzl C, Seiringer R. Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs. <i>Letters in Mathematical Physics</i>. 2012;100(2):119-138. doi:<a href=\"https://doi.org/10.1007/s11005-011-0535-4\">10.1007/s11005-011-0535-4</a>","apa":"Hainzl, C., &#38; Seiringer, R. (2012). Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs. <i>Letters in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s11005-011-0535-4\">https://doi.org/10.1007/s11005-011-0535-4</a>","chicago":"Hainzl, Christian, and Robert Seiringer. “Low Density Limit of BCS Theory and Bose-Einstein Condensation of Fermion Pairs.” <i>Letters in Mathematical Physics</i>. Springer, 2012. <a href=\"https://doi.org/10.1007/s11005-011-0535-4\">https://doi.org/10.1007/s11005-011-0535-4</a>.","ieee":"C. Hainzl and R. Seiringer, “Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs,” <i>Letters in Mathematical Physics</i>, vol. 100, no. 2. Springer, pp. 119–138, 2012.","ista":"Hainzl C, Seiringer R. 2012. Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs. Letters in Mathematical Physics. 100(2), 119–138.","mla":"Hainzl, Christian, and Robert Seiringer. “Low Density Limit of BCS Theory and Bose-Einstein Condensation of Fermion Pairs.” <i>Letters in Mathematical Physics</i>, vol. 100, no. 2, Springer, 2012, pp. 119–38, doi:<a href=\"https://doi.org/10.1007/s11005-011-0535-4\">10.1007/s11005-011-0535-4</a>.","short":"C. Hainzl, R. Seiringer, Letters in Mathematical Physics 100 (2012) 119–138."},"extern":1,"doi":"10.1007/s11005-011-0535-4","publication_status":"published","date_created":"2018-12-11T11:57:25Z","volume":100,"abstract":[{"lang":"eng","text":"We consider the low-density limit of a Fermi gas in the BCS approximation. We show that if the interaction potential allows for a two-particle bound state, the system at zero temperature is well approximated by the Gross-Pitaevskii functional, describing a Bose-Einstein condensate of fermion pairs."}],"publist_id":"4530","day":"01","publisher":"Springer","date_published":"2012-05-01T00:00:00Z","publication":"Letters in Mathematical Physics"},{"issue":"6","oa":1,"month":"07","year":"2012","intvolume":"        24","_id":"2398","type":"review","date_updated":"2020-07-14T12:45:40Z","title":"Quantum hypothesis testing and non-equilibrium statistical mechanics","main_file_link":[{"url":"http://arxiv.org/abs/1109.3804","open_access":"1"}],"publication":"Reviews in Mathematical Physics","date_published":"2012-07-01T00:00:00Z","publisher":"World Scientific Publishing","day":"01","publist_id":"4528","abstract":[{"text":"We extend the mathematical theory of quantum hypothesis testing to the general W*-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time.","lang":"eng"}],"volume":24,"publication_status":"published","date_created":"2018-12-11T11:57:26Z","doi":"10.1142/S0129055X12300026","citation":{"chicago":"Jakšić, Vojkan, Yoshiko Ogata, Claude Pillet, and Robert Seiringer. “Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2012. <a href=\"https://doi.org/10.1142/S0129055X12300026\">https://doi.org/10.1142/S0129055X12300026</a>.","apa":"Jakšić, V., Ogata, Y., Pillet, C., &#38; Seiringer, R. (2012). Quantum hypothesis testing and non-equilibrium statistical mechanics. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0129055X12300026\">https://doi.org/10.1142/S0129055X12300026</a>","ama":"Jakšić V, Ogata Y, Pillet C, Seiringer R. Quantum hypothesis testing and non-equilibrium statistical mechanics. <i>Reviews in Mathematical Physics</i>. 2012;24(6). doi:<a href=\"https://doi.org/10.1142/S0129055X12300026\">10.1142/S0129055X12300026</a>","short":"V. Jakšić, Y. Ogata, C. Pillet, R. Seiringer, Reviews in Mathematical Physics 24 (2012).","mla":"Jakšić, Vojkan, et al. “Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics.” <i>Reviews in Mathematical Physics</i>, vol. 24, no. 6, World Scientific Publishing, 2012, doi:<a href=\"https://doi.org/10.1142/S0129055X12300026\">10.1142/S0129055X12300026</a>.","ieee":"V. Jakšić, Y. Ogata, C. Pillet, and R. Seiringer, “Quantum hypothesis testing and non-equilibrium statistical mechanics,” <i>Reviews in Mathematical Physics</i>, vol. 24, no. 6. World Scientific Publishing, 2012.","ista":"Jakšić V, Ogata Y, Pillet C, Seiringer R. 2012. Quantum hypothesis testing and non-equilibrium statistical mechanics. Reviews in Mathematical Physics. 24(6)."},"extern":1,"author":[{"last_name":"Jakšić","full_name":"Jakšić, Vojkan","first_name":"Vojkan"},{"last_name":"Ogata","full_name":"Ogata, Yoshiko","first_name":"Yoshiko"},{"last_name":"Pillet","first_name":"Claude","full_name":"Pillet, Claude A"},{"last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","first_name":"Robert"}],"quality_controlled":0,"status":"public"},{"publication_status":"published","date_created":"2018-12-11T11:57:26Z","volume":2051,"doi":"10.1007/978-3-642-29511-9_2","alternative_title":["Lecture Notes in Mathematics"],"author":[{"orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"quality_controlled":0,"status":"public","extern":1,"citation":{"ieee":"R. Seiringer, “Cold quantum gases and bose einstein condensation,” in <i>Quantum Many Body Systems</i>, vol. 2051, V. Rivasseau, R. Seiringer, J. Solovej, and T. Spencer, Eds. Springer, 2012, pp. 55–92.","ista":"Seiringer R. 2012.Cold quantum gases and bose einstein condensation. In: Quantum Many Body Systems. Lecture Notes in Mathematics, vol. 2051, 55–92.","mla":"Seiringer, Robert. “Cold Quantum Gases and Bose Einstein Condensation.” <i>Quantum Many Body Systems</i>, edited by Vincent Rivasseau et al., vol. 2051, Springer, 2012, pp. 55–92, doi:<a href=\"https://doi.org/10.1007/978-3-642-29511-9_2\">10.1007/978-3-642-29511-9_2</a>.","short":"R. Seiringer, in:, V. Rivasseau, R. Seiringer, J. Solovej, T. Spencer (Eds.), Quantum Many Body Systems, Springer, 2012, pp. 55–92.","ama":"Seiringer R. Cold quantum gases and bose einstein condensation. In: Rivasseau V, Seiringer R, Solovej J, Spencer T, eds. <i>Quantum Many Body Systems</i>. Vol 2051. Springer; 2012:55-92. doi:<a href=\"https://doi.org/10.1007/978-3-642-29511-9_2\">10.1007/978-3-642-29511-9_2</a>","apa":"Seiringer, R. (2012). Cold quantum gases and bose einstein condensation. In V. Rivasseau, R. Seiringer, J. Solovej, &#38; T. Spencer (Eds.), <i>Quantum Many Body Systems</i> (Vol. 2051, pp. 55–92). Springer. <a href=\"https://doi.org/10.1007/978-3-642-29511-9_2\">https://doi.org/10.1007/978-3-642-29511-9_2</a>","chicago":"Seiringer, Robert. “Cold Quantum Gases and Bose Einstein Condensation.” In <i>Quantum Many Body Systems</i>, edited by Vincent Rivasseau, Robert Seiringer, Jan Solovej, and Thomas Spencer, 2051:55–92. Springer, 2012. <a href=\"https://doi.org/10.1007/978-3-642-29511-9_2\">https://doi.org/10.1007/978-3-642-29511-9_2</a>."},"date_published":"2012-01-01T00:00:00Z","publication":"Quantum Many Body Systems","day":"01","publisher":"Springer","publist_id":"4526","editor":[{"full_name":"Rivasseau, Vincent","first_name":"Vincent","last_name":"Rivasseau"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","first_name":"Robert","full_name":"Robert Seiringer","orcid":"0000-0002-6781-0521"},{"last_name":"Solovej","first_name":"Jan","full_name":"Solovej, Jan P"},{"last_name":"Spencer","first_name":"Thomas","full_name":"Spencer, Thomas"}],"abstract":[{"lang":"eng","text":"Bose–Einstein condensation (BEC) in cold atomic gases was first achieved experimentally in 1995 [1, 6]. After initial failed attempts with spin-polarized atomic hydrogen, the first successful demonstrations of this phenomenon used gases of rubidium and sodium atoms, respectively. Since then there has been a surge of activity in this field, with ingenious experiments putting forth more and more astonishing results about the behavior of matter at very cold temperatures.\n"}],"date_updated":"2021-01-12T06:57:14Z","_id":"2399","type":"book_chapter","title":"Cold quantum gases and bose einstein condensation","page":"55 - 92","month":"01","year":"2012","intvolume":"      2051"},{"title":"Sums of three squareful numbers","date_updated":"2021-01-12T06:57:15Z","type":"journal_article","_id":"240","month":"05","acknowledgement":"EP/E053262/1\tEngineering and Physical Sciences Research Council","year":"2012","intvolume":"        21","issue":"2","page":"204 - 211","quality_controlled":0,"author":[{"full_name":"Timothy Browning","first_name":"Timothy D","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning"},{"full_name":"Valckenborgh, K Van","first_name":"K Van","last_name":"Valckenborgh"}],"status":"public","citation":{"short":"T.D. Browning, K.V. Valckenborgh, Experimental Mathematics 21 (2012) 204–211.","mla":"Browning, Timothy D., and K. Van Valckenborgh. “Sums of Three Squareful Numbers.” <i>Experimental Mathematics</i>, vol. 21, no. 2, Taylor &#38; Francis, 2012, pp. 204–11, doi:<a href=\"https://doi.org/10.1080/10586458.2011.605733\">10.1080/10586458.2011.605733</a>.","ieee":"T. D. Browning and K. V. Valckenborgh, “Sums of three squareful numbers,” <i>Experimental Mathematics</i>, vol. 21, no. 2. Taylor &#38; Francis, pp. 204–211, 2012.","ista":"Browning TD, Valckenborgh KV. 2012. Sums of three squareful numbers. Experimental Mathematics. 21(2), 204–211.","apa":"Browning, T. D., &#38; Valckenborgh, K. V. (2012). Sums of three squareful numbers. <i>Experimental Mathematics</i>. Taylor &#38; Francis. <a href=\"https://doi.org/10.1080/10586458.2011.605733\">https://doi.org/10.1080/10586458.2011.605733</a>","chicago":"Browning, Timothy D, and K Van Valckenborgh. “Sums of Three Squareful Numbers.” <i>Experimental Mathematics</i>. Taylor &#38; Francis, 2012. <a href=\"https://doi.org/10.1080/10586458.2011.605733\">https://doi.org/10.1080/10586458.2011.605733</a>.","ama":"Browning TD, Valckenborgh KV. Sums of three squareful numbers. <i>Experimental Mathematics</i>. 2012;21(2):204-211. doi:<a href=\"https://doi.org/10.1080/10586458.2011.605733\">10.1080/10586458.2011.605733</a>"},"extern":1,"publication_status":"published","date_created":"2018-12-11T11:45:23Z","volume":21,"doi":"10.1080/10586458.2011.605733","publist_id":"7664","abstract":[{"text":"We investigate the frequency of positive squareful numbers x, y, z≤B for which x+y=z and present a conjecture concerning its asymptotic behavior.","lang":"eng"}],"date_published":"2012-05-23T00:00:00Z","publication":"Experimental Mathematics","day":"23","publisher":"Taylor & Francis"},{"intvolume":"       313","year":"2012","month":"07","oa":1,"page":"405 - 424","issue":"2","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1106.0729"}],"title":"Binding of polarons and atoms at threshold","type":"journal_article","_id":"2400","date_updated":"2021-01-12T06:57:15Z","abstract":[{"text":"If the polaron coupling constant α is large enough, bipolarons or multi-polarons will form. When passing through the critical α c from above, does the radius of the system simply get arbitrarily large or does it reach a maximum and then explode? We prove that it is always the latter. We also prove the analogous statement for the Pekar-Tomasevich (PT) approximation to the energy, in which case there is a solution to the PT equation at α c. Similarly, we show that the same phenomenon occurs for atoms, e. g., helium, at the critical value of the nuclear charge. Our proofs rely only on energy estimates, not on a detailed analysis of the Schrödinger equation, and are very general. They use the fact that the Coulomb repulsion decays like 1/r, while 'uncertainty principle' localization energies decay more rapidly, as 1/r 2.","lang":"eng"}],"publist_id":"4527","day":"01","publisher":"Springer","publication":"Communications in Mathematical Physics","date_published":"2012-07-01T00:00:00Z","citation":{"mla":"Frank, Rupert, et al. “Binding of Polarons and Atoms at Threshold.” <i>Communications in Mathematical Physics</i>, vol. 313, no. 2, Springer, 2012, pp. 405–24, doi:<a href=\"https://doi.org/10.1007/s00220-012-1436-9\">10.1007/s00220-012-1436-9</a>.","short":"R. Frank, É. Lieb, R. Seiringer, Communications in Mathematical Physics 313 (2012) 405–424.","ista":"Frank R, Lieb É, Seiringer R. 2012. Binding of polarons and atoms at threshold. Communications in Mathematical Physics. 313(2), 405–424.","ieee":"R. Frank, É. Lieb, and R. Seiringer, “Binding of polarons and atoms at threshold,” <i>Communications in Mathematical Physics</i>, vol. 313, no. 2. Springer, pp. 405–424, 2012.","chicago":"Frank, Rupert, Élliott Lieb, and Robert Seiringer. “Binding of Polarons and Atoms at Threshold.” <i>Communications in Mathematical Physics</i>. Springer, 2012. <a href=\"https://doi.org/10.1007/s00220-012-1436-9\">https://doi.org/10.1007/s00220-012-1436-9</a>.","apa":"Frank, R., Lieb, É., &#38; Seiringer, R. (2012). Binding of polarons and atoms at threshold. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-012-1436-9\">https://doi.org/10.1007/s00220-012-1436-9</a>","ama":"Frank R, Lieb É, Seiringer R. Binding of polarons and atoms at threshold. <i>Communications in Mathematical Physics</i>. 2012;313(2):405-424. doi:<a href=\"https://doi.org/10.1007/s00220-012-1436-9\">10.1007/s00220-012-1436-9</a>"},"extern":1,"quality_controlled":0,"author":[{"last_name":"Frank","first_name":"Rupert","full_name":"Frank, Rupert L"},{"first_name":"Élliott","full_name":"Lieb, Élliott H","last_name":"Lieb"},{"orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"status":"public","doi":"10.1007/s00220-012-1436-9","volume":313,"date_created":"2018-12-11T11:57:27Z","publication_status":"published"},{"month":"10","year":"2012","intvolume":"       149","issue":"1","oa":1,"page":"86 - 91","title":"Further implications of the Bessis-Moussa-Villani conjecture","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1206.0460"}],"type":"journal_article","_id":"2401","date_updated":"2021-01-12T06:57:16Z","publist_id":"4525","abstract":[{"text":"We find further implications of the BMV conjecture, which states that for hermitian matrices B≥0 and A, the function λ {mapping} Tr exp(A - λB) is the Laplace transform of a positive measure supported on [0,∞].","lang":"eng"}],"publication":"Journal of Statistical Physics","date_published":"2012-10-01T00:00:00Z","day":"01","publisher":"Springer","citation":{"chicago":"Lieb, Élliott, and Robert Seiringer. “Further Implications of the Bessis-Moussa-Villani Conjecture.” <i>Journal of Statistical Physics</i>. Springer, 2012. <a href=\"https://doi.org/10.1007/s10955-012-0585-8\">https://doi.org/10.1007/s10955-012-0585-8</a>.","apa":"Lieb, É., &#38; Seiringer, R. (2012). Further implications of the Bessis-Moussa-Villani conjecture. <i>Journal of Statistical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s10955-012-0585-8\">https://doi.org/10.1007/s10955-012-0585-8</a>","ama":"Lieb É, Seiringer R. Further implications of the Bessis-Moussa-Villani conjecture. <i>Journal of Statistical Physics</i>. 2012;149(1):86-91. doi:<a href=\"https://doi.org/10.1007/s10955-012-0585-8\">10.1007/s10955-012-0585-8</a>","mla":"Lieb, Élliott, and Robert Seiringer. “Further Implications of the Bessis-Moussa-Villani Conjecture.” <i>Journal of Statistical Physics</i>, vol. 149, no. 1, Springer, 2012, pp. 86–91, doi:<a href=\"https://doi.org/10.1007/s10955-012-0585-8\">10.1007/s10955-012-0585-8</a>.","short":"É. Lieb, R. Seiringer, Journal of Statistical Physics 149 (2012) 86–91.","ieee":"É. Lieb and R. Seiringer, “Further implications of the Bessis-Moussa-Villani conjecture,” <i>Journal of Statistical Physics</i>, vol. 149, no. 1. Springer, pp. 86–91, 2012.","ista":"Lieb É, Seiringer R. 2012. Further implications of the Bessis-Moussa-Villani conjecture. Journal of Statistical Physics. 149(1), 86–91."},"extern":1,"status":"public","author":[{"last_name":"Lieb","full_name":"Lieb, Élliott H","first_name":"Élliott"},{"last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","first_name":"Robert"}],"quality_controlled":0,"volume":149,"date_created":"2018-12-11T11:57:27Z","publication_status":"published","doi":"10.1007/s10955-012-0585-8"},{"main_file_link":[{"url":"http://arxiv.org/abs/1112.5617","open_access":"1"}],"title":"Lieb-Thirring inequality for a model of particles with point interactions","type":"journal_article","_id":"2402","date_updated":"2021-01-12T06:57:16Z","intvolume":"        53","year":"2012","month":"09","oa":1,"issue":"9","citation":{"apa":"Frank, R., &#38; Seiringer, R. (2012). Lieb-Thirring inequality for a model of particles with point interactions. <i>Journal of Mathematical Physics</i>. American Institute of Physics. <a href=\"https://doi.org/10.1063/1.3697416\">https://doi.org/10.1063/1.3697416</a>","chicago":"Frank, Rupert, and Robert Seiringer. “Lieb-Thirring Inequality for a Model of Particles with Point Interactions.” <i>Journal of Mathematical Physics</i>. American Institute of Physics, 2012. <a href=\"https://doi.org/10.1063/1.3697416\">https://doi.org/10.1063/1.3697416</a>.","ama":"Frank R, Seiringer R. Lieb-Thirring inequality for a model of particles with point interactions. <i>Journal of Mathematical Physics</i>. 2012;53(9). doi:<a href=\"https://doi.org/10.1063/1.3697416\">10.1063/1.3697416</a>","mla":"Frank, Rupert, and Robert Seiringer. “Lieb-Thirring Inequality for a Model of Particles with Point Interactions.” <i>Journal of Mathematical Physics</i>, vol. 53, no. 9, American Institute of Physics, 2012, doi:<a href=\"https://doi.org/10.1063/1.3697416\">10.1063/1.3697416</a>.","short":"R. Frank, R. Seiringer, Journal of Mathematical Physics 53 (2012).","ista":"Frank R, Seiringer R. 2012. Lieb-Thirring inequality for a model of particles with point interactions. Journal of Mathematical Physics. 53(9).","ieee":"R. Frank and R. Seiringer, “Lieb-Thirring inequality for a model of particles with point interactions,” <i>Journal of Mathematical Physics</i>, vol. 53, no. 9. American Institute of Physics, 2012."},"extern":1,"status":"public","quality_controlled":0,"author":[{"full_name":"Frank, Rupert L","first_name":"Rupert","last_name":"Frank"},{"last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","first_name":"Robert"}],"doi":"10.1063/1.3697416","volume":53,"date_created":"2018-12-11T11:57:27Z","publication_status":"published","abstract":[{"text":"We consider a model of quantum-mechanical particles interacting via point interactions of infinite scattering length. In the case of fermions we prove a Lieb-Thirring inequality for the energy, i.e., we show that the energy is bounded from below by a constant times the integral of the particle density to the power.","lang":"eng"}],"publist_id":"4524","publisher":"American Institute of Physics","day":"28","publication":"Journal of Mathematical Physics","date_published":"2012-09-28T00:00:00Z"},{"year":"2012","intvolume":"      2012","month":"11","oa":1,"issue":"11","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1207.7054"}],"title":"Disordered Bose-Einstein condensates with interaction in one dimension","_id":"2403","type":"journal_article","date_updated":"2021-01-12T06:57:16Z","abstract":[{"lang":"eng","text":"We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval in the Gross-Pitaevskii regime. We prove that Bose-Einstein condensation survives even a strong random potential with a high density of scatterers. The character of the wavefunction of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers and strong interactions the wavefunction extends over the whole interval. A high density of scatterers and weak interactions, on the other hand, lead to localization of the wavefunction in a fragmented subset of the interval."}],"publist_id":"4523","day":"01","publisher":"IOP Publishing Ltd.","publication":"Journal of Statistical Mechanics Theory and Experiment","date_published":"2012-11-01T00:00:00Z","extern":1,"citation":{"chicago":"Seiringer, Robert, Jakob Yngvason, and Valentin Zagrebnov. “Disordered Bose-Einstein Condensates with Interaction in One Dimension.” <i>Journal of Statistical Mechanics Theory and Experiment</i>. IOP Publishing Ltd., 2012. <a href=\"https://doi.org/10.1088/1742-5468/2012/11/P11007\">https://doi.org/10.1088/1742-5468/2012/11/P11007</a>.","apa":"Seiringer, R., Yngvason, J., &#38; Zagrebnov, V. (2012). Disordered Bose-Einstein condensates with interaction in one dimension. <i>Journal of Statistical Mechanics Theory and Experiment</i>. IOP Publishing Ltd. <a href=\"https://doi.org/10.1088/1742-5468/2012/11/P11007\">https://doi.org/10.1088/1742-5468/2012/11/P11007</a>","ama":"Seiringer R, Yngvason J, Zagrebnov V. Disordered Bose-Einstein condensates with interaction in one dimension. <i>Journal of Statistical Mechanics Theory and Experiment</i>. 2012;2012(11). doi:<a href=\"https://doi.org/10.1088/1742-5468/2012/11/P11007\">10.1088/1742-5468/2012/11/P11007</a>","short":"R. Seiringer, J. Yngvason, V. Zagrebnov, Journal of Statistical Mechanics Theory and Experiment 2012 (2012).","mla":"Seiringer, Robert, et al. “Disordered Bose-Einstein Condensates with Interaction in One Dimension.” <i>Journal of Statistical Mechanics Theory and Experiment</i>, vol. 2012, no. 11, IOP Publishing Ltd., 2012, doi:<a href=\"https://doi.org/10.1088/1742-5468/2012/11/P11007\">10.1088/1742-5468/2012/11/P11007</a>.","ista":"Seiringer R, Yngvason J, Zagrebnov V. 2012. Disordered Bose-Einstein condensates with interaction in one dimension. Journal of Statistical Mechanics Theory and Experiment. 2012(11).","ieee":"R. Seiringer, J. Yngvason, and V. Zagrebnov, “Disordered Bose-Einstein condensates with interaction in one dimension,” <i>Journal of Statistical Mechanics Theory and Experiment</i>, vol. 2012, no. 11. IOP Publishing Ltd., 2012."},"author":[{"full_name":"Robert Seiringer","first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer"},{"last_name":"Yngvason","full_name":"Yngvason, Jakob","first_name":"Jakob"},{"last_name":"Zagrebnov","first_name":"Valentin","full_name":"Zagrebnov, Valentin A"}],"status":"public","quality_controlled":0,"doi":"10.1088/1742-5468/2012/11/P11007","volume":2012,"date_created":"2018-12-11T11:57:28Z","publication_status":"published"},{"abstract":[{"lang":"eng","text":"The representation of integral binary forms as sums of two squares is discussed and applied to establish the Manin conjecture for certain Châtelet surfaces over ℚ."}],"publist_id":"7663","publisher":"Springer","day":"28","publication":"Israel Journal of Mathematics","date_published":"2012-02-28T00:00:00Z","citation":{"ama":"De La Bretèche R, Browning TD. Binary forms as sums of two squares and Châtelet surfaces. <i>Israel Journal of Mathematics</i>. 2012;191(2):973-1012. doi:<a href=\"https://doi.org/10.1007/s11856-012-0019-y\">10.1007/s11856-012-0019-y</a>","apa":"De La Bretèche, R., &#38; Browning, T. D. (2012). Binary forms as sums of two squares and Châtelet surfaces. <i>Israel Journal of Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s11856-012-0019-y\">https://doi.org/10.1007/s11856-012-0019-y</a>","chicago":"De La Bretèche, Régis, and Timothy D Browning. “Binary Forms as Sums of Two Squares and Châtelet Surfaces.” <i>Israel Journal of Mathematics</i>. Springer, 2012. <a href=\"https://doi.org/10.1007/s11856-012-0019-y\">https://doi.org/10.1007/s11856-012-0019-y</a>.","ieee":"R. De La Bretèche and T. D. Browning, “Binary forms as sums of two squares and Châtelet surfaces,” <i>Israel Journal of Mathematics</i>, vol. 191, no. 2. Springer, pp. 973–1012, 2012.","ista":"De La Bretèche R, Browning TD. 2012. Binary forms as sums of two squares and Châtelet surfaces. Israel Journal of Mathematics. 191(2), 973–1012.","short":"R. De La Bretèche, T.D. Browning, Israel Journal of Mathematics 191 (2012) 973–1012.","mla":"De La Bretèche, Régis, and Timothy D. Browning. “Binary Forms as Sums of Two Squares and Châtelet Surfaces.” <i>Israel Journal of Mathematics</i>, vol. 191, no. 2, Springer, 2012, pp. 973–1012, doi:<a href=\"https://doi.org/10.1007/s11856-012-0019-y\">10.1007/s11856-012-0019-y</a>."},"extern":1,"quality_controlled":0,"author":[{"last_name":"De La Bretèche","first_name":"Régis","full_name":"de la Bretèche, Régis"},{"orcid":"0000-0002-8314-0177","full_name":"Timothy Browning","first_name":"Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87"}],"status":"public","doi":"10.1007/s11856-012-0019-y","volume":191,"publication_status":"published","date_created":"2018-12-11T11:45:23Z","intvolume":"       191","year":"2012","month":"02","page":"973 - 1012","issue":"2","title":"Binary forms as sums of two squares and Châtelet surfaces","type":"journal_article","_id":"241","date_updated":"2021-01-12T06:57:19Z"},{"ddc":["570","576"],"type":"journal_article","page":"1319 - 1334","issue":"5","intvolume":"        29","pubrep_id":"384","month":"05","license":"https://creativecommons.org/licenses/by-nc/4.0/","publication_status":"published","quality_controlled":"1","citation":{"ama":"Ebersberger I, De Matos Simoes R, Kupczok A, et al. A consistent phylogenetic backbone for the fungi. <i>Molecular Biology and Evolution</i>. 2012;29(5):1319-1334. doi:<a href=\"https://doi.org/10.1093/molbev/msr285\">10.1093/molbev/msr285</a>","apa":"Ebersberger, I., De Matos Simoes, R., Kupczok, A., Gube, M., Kothe, E., Voigt, K., &#38; Von Haeseler, A. (2012). A consistent phylogenetic backbone for the fungi. <i>Molecular Biology and Evolution</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/molbev/msr285\">https://doi.org/10.1093/molbev/msr285</a>","chicago":"Ebersberger, Ingo, Ricardo De Matos Simoes, Anne Kupczok, Matthias Gube, Erika Kothe, Kerstin Voigt, and Arndt Von Haeseler. “A Consistent Phylogenetic Backbone for the Fungi.” <i>Molecular Biology and Evolution</i>. Oxford University Press, 2012. <a href=\"https://doi.org/10.1093/molbev/msr285\">https://doi.org/10.1093/molbev/msr285</a>.","ieee":"I. Ebersberger <i>et al.</i>, “A consistent phylogenetic backbone for the fungi,” <i>Molecular Biology and Evolution</i>, vol. 29, no. 5. Oxford University Press, pp. 1319–1334, 2012.","ista":"Ebersberger I, De Matos Simoes R, Kupczok A, Gube M, Kothe E, Voigt K, Von Haeseler A. 2012. A consistent phylogenetic backbone for the fungi. Molecular Biology and Evolution. 29(5), 1319–1334.","mla":"Ebersberger, Ingo, et al. “A Consistent Phylogenetic Backbone for the Fungi.” <i>Molecular Biology and Evolution</i>, vol. 29, no. 5, Oxford University Press, 2012, pp. 1319–34, doi:<a href=\"https://doi.org/10.1093/molbev/msr285\">10.1093/molbev/msr285</a>.","short":"I. Ebersberger, R. De Matos Simoes, A. Kupczok, M. Gube, E. Kothe, K. Voigt, A. Von Haeseler, Molecular Biology and Evolution 29 (2012) 1319–1334."},"publisher":"Oxford University Press","file_date_updated":"2020-07-14T12:45:40Z","publication":"Molecular Biology and Evolution","scopus_import":1,"file":[{"relation":"main_file","file_size":754922,"date_created":"2018-12-12T10:13:30Z","date_updated":"2020-07-14T12:45:40Z","file_name":"IST-2015-384-v1+1_Mol_Biol_Evol-2012-Ebersberger-1319-34.pdf","checksum":"d565dcac27d1736c0c378ea6fcf22d69","content_type":"application/pdf","access_level":"open_access","creator":"system","file_id":"5013"}],"abstract":[{"lang":"eng","text":"The kingdom of fungi provides model organisms for biotechnology, cell biology, genetics, and life sciences in general. Only when their phylogenetic relationships are stably resolved, can individual results from fungal research be integrated into a holistic picture of biology. However, and despite recent progress, many deep relationships within the fungi remain unclear. Here, we present the first phylogenomic study of an entire eukaryotic kingdom that uses a consistency criterion to strengthen phylogenetic conclusions. We reason that branches (splits) recovered with independent data and different tree reconstruction methods are likely to reflect true evolutionary relationships. Two complementary phylogenomic data sets based on 99 fungal genomes and 109 fungal expressed sequence tag (EST) sets analyzed with four different tree reconstruction methods shed light from different angles on the fungal tree of life. Eleven additional data sets address specifically the phylogenetic position of Blastocladiomycota, Ustilaginomycotina, and Dothideomycetes, respectively. The combined evidence from the resulting trees supports the deep-level stability of the fungal groups toward a comprehensive natural system of the fungi. In addition, our analysis reveals methodologically interesting aspects. Enrichment for EST encoded data-a common practice in phylogenomic analyses-introduces a strong bias toward slowly evolving and functionally correlated genes. Consequently, the generalization of phylogenomic data sets as collections of randomly selected genes cannot be taken for granted. A thorough characterization of the data to assess possible influences on the tree reconstruction should therefore become a standard in phylogenomic analyses."}],"publist_id":"4515","department":[{"_id":"JoBo"}],"language":[{"iso":"eng"}],"date_updated":"2021-01-12T06:57:19Z","_id":"2411","title":"A consistent phylogenetic backbone for the fungi","oa":1,"year":"2012","has_accepted_license":"1","doi":"10.1093/molbev/msr285","date_created":"2018-12-11T11:57:30Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","volume":29,"oa_version":"Published Version","author":[{"last_name":"Ebersberger","first_name":"Ingo","full_name":"Ebersberger, Ingo"},{"first_name":"Ricardo","full_name":"De Matos Simoes, Ricardo","last_name":"De Matos Simoes"},{"first_name":"Anne","full_name":"Kupczok, Anne","last_name":"Kupczok","id":"2BB22BC2-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Gube, Matthias","first_name":"Matthias","last_name":"Gube"},{"last_name":"Kothe","first_name":"Erika","full_name":"Kothe, Erika"},{"first_name":"Kerstin","full_name":"Voigt, Kerstin","last_name":"Voigt"},{"last_name":"Von Haeseler","full_name":"Von Haeseler, Arndt","first_name":"Arndt"}],"tmp":{"short":"CC BY-NC (4.0)","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","image":"/images/cc_by_nc.png"},"status":"public","day":"01","date_published":"2012-05-01T00:00:00Z"},{"publist_id":"7662","abstract":[{"lang":"eng","text":"We investigate the first and second moments of shifted convolutions of the generalized divisor function d 3(n)."}],"date_published":"2012-10-01T00:00:00Z","publication":"Proceedings of the Edinburgh Mathematical Society","day":"01","publisher":"Cambridge University Press","status":"public","author":[{"last_name":"Baier","first_name":"Stephan","full_name":"Baier, Stephan"},{"orcid":"0000-0002-8314-0177","full_name":"Timothy Browning","first_name":"Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Marasingha, Gihan","first_name":"Gihan","last_name":"Marasingha"},{"last_name":"Zhao","first_name":"Liangyi","full_name":"Zhao, Liangyi"}],"quality_controlled":0,"citation":{"ama":"Baier S, Browning TD, Marasingha G, Zhao L. Averages of shifted convolutions of d3 (n). <i>Proceedings of the Edinburgh Mathematical Society</i>. 2012;55(3):551-576. doi:<a href=\"https://doi.org/10.1017/S001309151100037X\">10.1017/S001309151100037X</a>","apa":"Baier, S., Browning, T. D., Marasingha, G., &#38; Zhao, L. (2012). Averages of shifted convolutions of d3 (n). <i>Proceedings of the Edinburgh Mathematical Society</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/S001309151100037X\">https://doi.org/10.1017/S001309151100037X</a>","chicago":"Baier, Stephan, Timothy D Browning, Gihan Marasingha, and Liangyi Zhao. “Averages of Shifted Convolutions of D3 (N).” <i>Proceedings of the Edinburgh Mathematical Society</i>. Cambridge University Press, 2012. <a href=\"https://doi.org/10.1017/S001309151100037X\">https://doi.org/10.1017/S001309151100037X</a>.","ieee":"S. Baier, T. D. Browning, G. Marasingha, and L. Zhao, “Averages of shifted convolutions of d3 (n),” <i>Proceedings of the Edinburgh Mathematical Society</i>, vol. 55, no. 3. Cambridge University Press, pp. 551–576, 2012.","ista":"Baier S, Browning TD, Marasingha G, Zhao L. 2012. Averages of shifted convolutions of d3 (n). Proceedings of the Edinburgh Mathematical Society. 55(3), 551–576.","short":"S. Baier, T.D. Browning, G. Marasingha, L. Zhao, Proceedings of the Edinburgh Mathematical Society 55 (2012) 551–576.","mla":"Baier, Stephan, et al. “Averages of Shifted Convolutions of D3 (N).” <i>Proceedings of the Edinburgh Mathematical Society</i>, vol. 55, no. 3, Cambridge University Press, 2012, pp. 551–76, doi:<a href=\"https://doi.org/10.1017/S001309151100037X\">10.1017/S001309151100037X</a>."},"extern":1,"date_created":"2018-12-11T11:45:23Z","publication_status":"published","volume":55,"doi":"10.1017/S001309151100037X","month":"10","acknowledgement":"EP/E053262/1\tEngineering and Physical Sciences Research Council","year":"2012","intvolume":"        55","issue":"3","page":"551 - 576","oa":1,"title":"Averages of shifted convolutions of d3 (n)","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1101.5464"}],"date_updated":"2021-01-12T06:57:23Z","_id":"242","type":"journal_article"},{"year":"2012","intvolume":"        22","month":"08","page":"1124 - 1190","issue":"5","title":"Quadratic polynomials represented by norm forms","type":"journal_article","_id":"243","date_updated":"2021-01-12T06:57:26Z","abstract":[{"text":"Let P(t) ∈ ℚ[t] be an irreducible quadratic polynomial and suppose that K is a quartic extension of ℚ containing the roots of P(t). Let N K/ℚ(X) be a full norm form for the extension K/ℚ. We show that the variety P(t) =N K/ℚ(X)≠ 0 satisfies the Hasse principle and weak approximation. The proof uses analytic methods.","lang":"eng"}],"publist_id":"7661","publisher":"Springer Basel","day":"25","publication":"Geometric and Functional Analysis","date_published":"2012-08-25T00:00:00Z","citation":{"ama":"Browning TD, Heath Brown R. Quadratic polynomials represented by norm forms. <i>Geometric and Functional Analysis</i>. 2012;22(5):1124-1190. doi:<a href=\"https://doi.org/10.1007/s00039-012-0168-5\">10.1007/s00039-012-0168-5</a>","chicago":"Browning, Timothy D, and Roger Heath Brown. “Quadratic Polynomials Represented by Norm Forms.” <i>Geometric and Functional Analysis</i>. Springer Basel, 2012. <a href=\"https://doi.org/10.1007/s00039-012-0168-5\">https://doi.org/10.1007/s00039-012-0168-5</a>.","apa":"Browning, T. D., &#38; Heath Brown, R. (2012). Quadratic polynomials represented by norm forms. <i>Geometric and Functional Analysis</i>. Springer Basel. <a href=\"https://doi.org/10.1007/s00039-012-0168-5\">https://doi.org/10.1007/s00039-012-0168-5</a>","ista":"Browning TD, Heath Brown R. 2012. Quadratic polynomials represented by norm forms. Geometric and Functional Analysis. 22(5), 1124–1190.","ieee":"T. D. Browning and R. Heath Brown, “Quadratic polynomials represented by norm forms,” <i>Geometric and Functional Analysis</i>, vol. 22, no. 5. Springer Basel, pp. 1124–1190, 2012.","short":"T.D. Browning, R. Heath Brown, Geometric and Functional Analysis 22 (2012) 1124–1190.","mla":"Browning, Timothy D., and Roger Heath Brown. “Quadratic Polynomials Represented by Norm Forms.” <i>Geometric and Functional Analysis</i>, vol. 22, no. 5, Springer Basel, 2012, pp. 1124–90, doi:<a href=\"https://doi.org/10.1007/s00039-012-0168-5\">10.1007/s00039-012-0168-5</a>."},"extern":1,"quality_controlled":0,"status":"public","author":[{"last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","first_name":"Timothy D","full_name":"Timothy Browning"},{"full_name":"Heath-Brown, Roger","first_name":"Roger","last_name":"Heath Brown"}],"doi":"10.1007/s00039-012-0168-5","volume":22,"date_created":"2018-12-11T11:45:24Z","publication_status":"published"},{"publication":"Discrete & Computational Geometry","date_published":"2012-03-01T00:00:00Z","publisher":"Springer","day":"01","publist_id":"4468","abstract":[{"lang":"eng","text":"The colored Tverberg theorem asserts that for eve;ry d and r there exists t=t(d,r) such that for every set C ⊂ ℝ d of cardinality (d + 1)t, partitioned into t-point subsets C 1, C 2,...,C d+1 (which we think of as color classes; e. g., the points of C 1 are red, the points of C 2 blue, etc.), there exist r disjoint sets R 1, R 2,...,R r⊆C that are rainbow, meaning that {pipe}R i∩C j{pipe}≤1 for every i,j, and whose convex hulls all have a common point. All known proofs of this theorem are topological. We present a geometric version of a recent beautiful proof by Blagojević, Matschke, and Ziegler, avoiding a direct use of topological methods. The purpose of this de-topologization is to make the proof more concrete and intuitive, and accessible to a wider audience."}],"volume":47,"publication_status":"published","date_created":"2018-12-11T11:57:39Z","doi":"10.1007/s00454-011-9368-2","extern":1,"citation":{"ieee":"J. Matoušek, M. Tancer, and U. Wagner, “A geometric proof of the colored Tverberg theorem,” <i>Discrete &#38; Computational Geometry</i>, vol. 47, no. 2. Springer, pp. 245–265, 2012.","ista":"Matoušek J, Tancer M, Wagner U. 2012. A geometric proof of the colored Tverberg theorem. Discrete &#38; Computational Geometry. 47(2), 245–265.","short":"J. Matoušek, M. Tancer, U. Wagner, Discrete &#38; Computational Geometry 47 (2012) 245–265.","mla":"Matoušek, Jiří, et al. “A Geometric Proof of the Colored Tverberg Theorem.” <i>Discrete &#38; Computational Geometry</i>, vol. 47, no. 2, Springer, 2012, pp. 245–65, doi:<a href=\"https://doi.org/10.1007/s00454-011-9368-2\">10.1007/s00454-011-9368-2</a>.","ama":"Matoušek J, Tancer M, Wagner U. A geometric proof of the colored Tverberg theorem. <i>Discrete &#38; Computational Geometry</i>. 2012;47(2):245-265. doi:<a href=\"https://doi.org/10.1007/s00454-011-9368-2\">10.1007/s00454-011-9368-2</a>","chicago":"Matoušek, Jiří, Martin Tancer, and Uli Wagner. “A Geometric Proof of the Colored Tverberg Theorem.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2012. <a href=\"https://doi.org/10.1007/s00454-011-9368-2\">https://doi.org/10.1007/s00454-011-9368-2</a>.","apa":"Matoušek, J., Tancer, M., &#38; Wagner, U. (2012). A geometric proof of the colored Tverberg theorem. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-011-9368-2\">https://doi.org/10.1007/s00454-011-9368-2</a>"},"author":[{"first_name":"Jiří","full_name":"Matoušek, Jiří","last_name":"Matoušek"},{"last_name":"Tancer","id":"38AC689C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1191-6714","full_name":"Martin Tancer","first_name":"Martin"},{"first_name":"Uli","full_name":"Uli Wagner","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner"}],"status":"public","quality_controlled":0,"issue":"2","page":"245 - 265","month":"03","intvolume":"        47","year":"2012","acknowledgement":"We would like to thank Marek Krcál for useful discussions at initial stages of this research. We also thank Günter M. Ziegler for valuable comments, and Peter Landweber and two anonymous referees for detailed comments and corrections that greatly helped to improve the presentation. In particular, we are indebted to one of the referees for pointing out to us reference [19]. M. Tancer is supported by the grants SVV-2010-261313 (Discrete Methods and Algorithms) and GAUK 49209. U. Wagner’s research is supported by the Swiss National Science Foundation (SNF Projects 200021- 125309 and 200020-125027). ","type":"journal_article","_id":"2438","date_updated":"2021-01-12T06:57:29Z","title":"A geometric proof of the colored Tverberg theorem"},{"page":"566 - 573","issue":"5","intvolume":"        46","year":"2012","month":"07","date_updated":"2021-01-12T06:57:29Z","_id":"2439","type":"journal_article","title":"Absolute approximation of Tukey depth: Theory and experiments","publisher":"Elsevier","day":"01","date_published":"2012-07-01T00:00:00Z","publication":"Computational Geometry: Theory and Applications","abstract":[{"lang":"eng","text":"A Monte Carlo approximation algorithm for the Tukey depth problem in high dimensions is introduced. The algorithm is a generalization of an algorithm presented by Rousseeuw and Struyf (1998) . The performance of this algorithm is studied both analytically and experimentally."}],"publist_id":"4467","doi":"10.1016/j.comgeo.2012.03.001","date_created":"2018-12-11T11:57:40Z","publication_status":"published","volume":46,"status":"public","author":[{"last_name":"Chen","first_name":"Dan","full_name":"Chen, Dan"},{"last_name":"Morin","first_name":"Pat","full_name":"Morin, Pat"},{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","full_name":"Uli Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568"}],"quality_controlled":0,"citation":{"mla":"Chen, Dan, et al. “Absolute Approximation of Tukey Depth: Theory and Experiments.” <i>Computational Geometry: Theory and Applications</i>, vol. 46, no. 5, Elsevier, 2012, pp. 566–73, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2012.03.001\">10.1016/j.comgeo.2012.03.001</a>.","short":"D. Chen, P. Morin, U. Wagner, Computational Geometry: Theory and Applications 46 (2012) 566–573.","ista":"Chen D, Morin P, Wagner U. 2012. Absolute approximation of Tukey depth: Theory and experiments. Computational Geometry: Theory and Applications. 46(5), 566–573.","ieee":"D. Chen, P. Morin, and U. Wagner, “Absolute approximation of Tukey depth: Theory and experiments,” <i>Computational Geometry: Theory and Applications</i>, vol. 46, no. 5. Elsevier, pp. 566–573, 2012.","chicago":"Chen, Dan, Pat Morin, and Uli Wagner. “Absolute Approximation of Tukey Depth: Theory and Experiments.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2012. <a href=\"https://doi.org/10.1016/j.comgeo.2012.03.001\">https://doi.org/10.1016/j.comgeo.2012.03.001</a>.","apa":"Chen, D., Morin, P., &#38; Wagner, U. (2012). Absolute approximation of Tukey depth: Theory and experiments. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2012.03.001\">https://doi.org/10.1016/j.comgeo.2012.03.001</a>","ama":"Chen D, Morin P, Wagner U. Absolute approximation of Tukey depth: Theory and experiments. <i>Computational Geometry: Theory and Applications</i>. 2012;46(5):566-573. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2012.03.001\">10.1016/j.comgeo.2012.03.001</a>"},"extern":1},{"extern":1,"citation":{"mla":"Browning, Timothy D., and Alan Haynes. “Incomplete Kloosterman Sums and Multiplicative Inverses in Short Intervals.” <i>International Journal of Number Theory</i>, vol. 9, no. 2, World Scientific Publishing, 2012, pp. 481–86, doi:<a href=\"https://doi.org/ https://doi.org/10.1142/S1793042112501448\"> https://doi.org/10.1142/S1793042112501448</a>.","short":"T.D. Browning, A. Haynes, International Journal of Number Theory 9 (2012) 481–486.","ista":"Browning TD, Haynes A. 2012. Incomplete kloosterman sums and multiplicative inverses in short intervals. International Journal of Number Theory. 9(2), 481–486.","ieee":"T. D. Browning and A. Haynes, “Incomplete kloosterman sums and multiplicative inverses in short intervals,” <i>International Journal of Number Theory</i>, vol. 9, no. 2. World Scientific Publishing, pp. 481–486, 2012.","apa":"Browning, T. D., &#38; Haynes, A. (2012). Incomplete kloosterman sums and multiplicative inverses in short intervals. <i>International Journal of Number Theory</i>. World Scientific Publishing. <a href=\"https://doi.org/ https://doi.org/10.1142/S1793042112501448\">https://doi.org/ https://doi.org/10.1142/S1793042112501448</a>","chicago":"Browning, Timothy D, and Alan Haynes. “Incomplete Kloosterman Sums and Multiplicative Inverses in Short Intervals.” <i>International Journal of Number Theory</i>. World Scientific Publishing, 2012. <a href=\"https://doi.org/ https://doi.org/10.1142/S1793042112501448\">https://doi.org/ https://doi.org/10.1142/S1793042112501448</a>.","ama":"Browning TD, Haynes A. Incomplete kloosterman sums and multiplicative inverses in short intervals. <i>International Journal of Number Theory</i>. 2012;9(2):481-486. doi:<a href=\"https://doi.org/ https://doi.org/10.1142/S1793042112501448\"> https://doi.org/10.1142/S1793042112501448</a>"},"status":"public","author":[{"last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Timothy Browning","first_name":"Timothy D"},{"last_name":"Haynes","full_name":"Haynes, Alan K","first_name":"Alan"}],"quality_controlled":0,"doi":" https://doi.org/10.1142/S1793042112501448","volume":9,"publication_status":"published","date_created":"2018-12-11T11:45:24Z","abstract":[{"lang":"eng","text":"We investigate the solubility of the congruence xy ≡ 1 (mod p), where p is a prime and x, y are restricted to lie in suitable short intervals. Our work relies on a mean value theorem for incomplete Kloosterman sums."}],"publist_id":"7660","day":"30","publisher":"World Scientific Publishing","publication":"International Journal of Number Theory","date_published":"2012-11-30T00:00:00Z","main_file_link":[{"url":"https://arxiv.org/abs/1204.6374","open_access":"1"}],"title":"Incomplete kloosterman sums and multiplicative inverses in short intervals","type":"journal_article","_id":"244","date_updated":"2021-01-12T06:57:30Z","acknowledgement":"EP/E053262/1\tEngineering and Physical Sciences Research Council\tEPSRC,\nEP/J00149X/1\tEngineering and Physical Sciences Research Council\tEPSRC\t","intvolume":"         9","year":"2012","month":"11","oa":1,"page":"481 - 486","issue":"2"},{"main_file_link":[{"open_access":"0","url":"http://arxiv.org/abs/1105.6257"}],"title":"Computing all maps into a sphere","date_updated":"2021-01-12T06:57:30Z","_id":"2440","type":"conference","conference":{"name":"SODA: Symposium on Discrete Algorithms"},"year":"2012","month":"01","page":"1 - 10","author":[{"last_name":"Čadek","full_name":"Čadek, Martin","first_name":"Martin"},{"id":"33E21118-F248-11E8-B48F-1D18A9856A87","last_name":"Krcál","first_name":"Marek","full_name":"Marek Krcál"},{"full_name":"Matoušek, Jiří","first_name":"Jiří","last_name":"Matoušek"},{"last_name":"Sergeraert","full_name":"Sergeraert, Francis","first_name":"Francis"},{"last_name":"Vokřínek","first_name":"Lukáš","full_name":"Vokřínek, Lukáš"},{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","full_name":"Uli Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568"}],"status":"public","quality_controlled":0,"citation":{"ama":"Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. Computing all maps into a sphere. In: SIAM; 2012:1-10.","chicago":"Čadek, Martin, Marek Krcál, Jiří Matoušek, Francis Sergeraert, Lukáš Vokřínek, and Uli Wagner. “Computing All Maps into a Sphere,” 1–10. SIAM, 2012.","apa":"Čadek, M., Krcál, M., Matoušek, J., Sergeraert, F., Vokřínek, L., &#38; Wagner, U. (2012). Computing all maps into a sphere (pp. 1–10). Presented at the SODA: Symposium on Discrete Algorithms, SIAM.","ieee":"M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, and U. Wagner, “Computing all maps into a sphere,” presented at the SODA: Symposium on Discrete Algorithms, 2012, pp. 1–10.","ista":"Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. 2012. Computing all maps into a sphere. SODA: Symposium on Discrete Algorithms, 1–10.","short":"M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, U. Wagner, in:, SIAM, 2012, pp. 1–10.","mla":"Čadek, Martin, et al. <i>Computing All Maps into a Sphere</i>. SIAM, 2012, pp. 1–10."},"extern":1,"date_created":"2018-12-11T11:57:40Z","publication_status":"published","abstract":[{"text":"We present an algorithm for computing [X, Y], i.e., all homotopy classes of continuous maps X → Y, where X, Y are topological spaces given as finite simplicial complexes, Y is (d - 1)-connected for some d ≥ 2 (for example, Y can be the d-dimensional sphere S d), and dim X ≤ 2d - 2. These conditions on X, Y guarantee that [X, Y] has a natural structure of a finitely generated Abelian group, and the algorithm finds generators and relations for it. We combine several tools and ideas from homotopy theory (such as Postnikov systems, simplicial sets, and obstruction theory) with algorithmic tools from effective algebraic topology (objects with effective homology). We hope that a further extension of the methods developed here will yield an algorithm for computing, in some cases of interest, the ℤ 2-index, which is a quantity playing a prominent role in Borsuk-Ulam style applications of topology in combinatorics and geometry, e.g., in topological lower bounds for the chromatic number of a graph. In a certain range of dimensions, deciding the embeddability of a simplicial complex into ℝ d also amounts to a ℤ 2-index computation. This is the main motivation of our work. We believe that investigating the computational complexity of questions in homotopy theory and similar areas presents a fascinating research area, and we hope that our work may help bridge the cultural gap between algebraic topology and theoretical computer science.","lang":"eng"}],"publist_id":"4466","day":"01","publisher":"SIAM","date_published":"2012-01-01T00:00:00Z"},{"title":"On Laplacians of random complexes","conference":{"name":"SGC: Symposuim on Computational Geometry"},"_id":"2441","type":"conference","date_updated":"2021-01-12T06:57:30Z","month":"06","year":"2012","page":"151 - 160","extern":1,"citation":{"ama":"Gundert A, Wagner U. On Laplacians of random complexes. In: ACM; 2012:151-160. doi:<a href=\"https://doi.org/10.1145/2261250.2261272\">10.1145/2261250.2261272</a>","chicago":"Gundert, Anna, and Uli Wagner. “On Laplacians of Random Complexes,” 151–60. ACM, 2012. <a href=\"https://doi.org/10.1145/2261250.2261272\">https://doi.org/10.1145/2261250.2261272</a>.","apa":"Gundert, A., &#38; Wagner, U. (2012). On Laplacians of random complexes (pp. 151–160). Presented at the SGC: Symposuim on Computational Geometry, ACM. <a href=\"https://doi.org/10.1145/2261250.2261272\">https://doi.org/10.1145/2261250.2261272</a>","ieee":"A. Gundert and U. Wagner, “On Laplacians of random complexes,” presented at the SGC: Symposuim on Computational Geometry, 2012, pp. 151–160.","ista":"Gundert A, Wagner U. 2012. On Laplacians of random complexes. SGC: Symposuim on Computational Geometry, 151–160.","mla":"Gundert, Anna, and Uli Wagner. <i>On Laplacians of Random Complexes</i>. ACM, 2012, pp. 151–60, doi:<a href=\"https://doi.org/10.1145/2261250.2261272\">10.1145/2261250.2261272</a>.","short":"A. Gundert, U. Wagner, in:, ACM, 2012, pp. 151–160."},"author":[{"first_name":"Anna","full_name":"Gundert, Anna","last_name":"Gundert"},{"last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","first_name":"Uli","full_name":"Uli Wagner"}],"quality_controlled":0,"status":"public","publication_status":"published","date_created":"2018-12-11T11:57:41Z","doi":"10.1145/2261250.2261272","publist_id":"4464","abstract":[{"lang":"eng","text":"Eigenvalues associated to graphs are a well-studied subject. In particular the spectra of the adjacency matrix and of the Laplacian of random graphs G(n, p) are known quite precisely. We consider generalizations of these matrices to simplicial complexes of higher dimensions and study their eigenvalues for the Linial-Meshulam model X k(n, p) of random k-dimensional simplicial complexes on n vertices. We show that for p = Ω(log n/n), the eigenvalues of both, the higher-dimensional adjacency matrix and the Laplacian, are a.a.s. sharply concentrated around two values. In a second part of the paper, we discuss a possible higherdimensional analogue of the Discrete Cheeger Inequality. This fundamental inequality expresses a close relationship between the eigenvalues of a graph and its combinatorial expansion properties; in particular, spectral expansion (a large eigenvalue gap) implies edge expansion. Recently, a higher-dimensional analogue of edge expansion for simplicial complexes was introduced by Gromov, and independently by Linial, Meshulam and Wallach and by Newman and Rabinovich. It is natural to ask whether there is a higher-dimensional version of Cheeger's inequality. We show that the most straightforward version of a higher-dimensional Cheeger inequality fails: for every k &gt; 1, there is an infinite family of k-dimensional complexes that are spectrally expanding (there is a large eigenvalue gap for the Laplacian) but not combinatorially expanding."}],"date_published":"2012-06-01T00:00:00Z","publisher":"ACM","day":"01"}]