@article{13177,
  abstract     = {In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities and that the total measure is finite. In this sense, the associated operators on these graphs display similarities to elliptic operators on bounded domains in the continuum. Specifically, we prove lower bounds on the eigenvalue growth and show by examples that corresponding upper bounds cannot be established.},
  author       = {Hua, Bobo and Keller, Matthias and Schwarz, Michael and Wirth, Melchior},
  issn         = {1088-6826},
  journal      = {Proceedings of the American Mathematical Society},
  number       = {8},
  pages        = {3401--3414},
  publisher    = {American Mathematical Society},
  title        = {{Sobolev-type inequalities and eigenvalue growth on graphs with finite measure}},
  doi          = {10.1090/proc/14361},
  volume       = {151},
  year         = {2023},
}

@article{12427,
  abstract     = {Let k be a number field and X a smooth, geometrically integral quasi-projective variety over k. For any linear algebraic group G over k and any G-torsor g : Z → X, we observe that if the étale-Brauer obstruction is the only one for strong approximation off a finite set of places S for all twists of Z by elements in H^1(k, G), then the étale-Brauer obstruction is the only one for strong approximation off a finite set of places S for X. As an application, we show that any homogeneous space of the form G/H with G a connected linear algebraic group over k satisfies strong approximation off the infinite places with étale-Brauer obstruction, under some compactness assumptions when k is totally real. We also prove more refined strong approximation results for homogeneous spaces of the form G/H with G semisimple simply connected and H finite, using the theory of torsors and descent.},
  author       = {Balestrieri, Francesca},
  issn         = {1088-6826},
  journal      = {Proceedings of the American Mathematical Society},
  number       = {3},
  pages        = {907--914},
  publisher    = {American Mathematical Society},
  title        = {{Some remarks on strong approximation and applications to homogeneous spaces of linear algebraic groups}},
  doi          = {10.1090/proc/15239},
  volume       = {151},
  year         = {2023},
}

@article{8773,
  abstract     = {Let g be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose dimension is given by the cardinality of the Weyl group of g. We also describe a procedure for parabolically inducing contravariant forms. As a corollary, we deduce the existence of the Shapovalov form on a Verma module, and provide a formula for the dimension of the space of contravariant forms on the degenerate Whittaker modules M(χ,η) introduced by McDowell.},
  author       = {Brown, Adam and Romanov, Anna},
  issn         = {1088-6826},
  journal      = {Proceedings of the American Mathematical Society},
  keywords     = {Applied Mathematics, General Mathematics},
  number       = {1},
  pages        = {37--52},
  publisher    = {American Mathematical Society},
  title        = {{Contravariant forms on Whittaker modules}},
  doi          = {10.1090/proc/15205},
  volume       = {149},
  year         = {2021},
}

@article{6986,
  abstract     = {Li-Nadler proposed a conjecture about traces of Hecke categories, which implies the semistable part of the Betti geometric Langlands conjecture of Ben-Zvi-Nadler in genus 1. We prove a Weyl group analogue of this conjecture. Our theorem holds in the natural generality of reflection groups in Euclidean or hyperbolic space. As a corollary, we give an expression of the centralizer of a finite order element in a reflection group using homotopy theory. },
  author       = {Li, Penghui},
  issn         = {1088-6826},
  journal      = {Proceedings of the American Mathematical Society},
  number       = {11},
  pages        = {4597--4604},
  publisher    = {AMS},
  title        = {{A colimit of traces of reflection groups}},
  doi          = {10.1090/proc/14586},
  volume       = {147},
  year         = {2019},
}