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Events and Activities

Members' Colloquium

December 15, 2025 | 1:30pm - 2:30pm
Add to calendar 12/15/2025 13:3012/15/2025 14:30Members' Colloquiumuse-titleTopic: Fundamental Groups of Algebraic Varieties and the Shafarevich Conjecture Speakers: Benjamin Thomas Bakker, Institute for Advanced Study More: https://www.ias.edu/math/events/members-colloquium-96 The fundamental group $\pi_1(X)$ is an important invariant of a complex algebraic variety X.  Despite its topological nature, it is closely connected to the geometry of many algebraic structures on X.  In this talk I want to discuss two elementary questions involving the fundamental group: (1) How many simply-connected algebraic subvarieties does X contain? (2) How many global holomorphic functions does the universal cover $\tilde{X}$ have? The second question is related to a famous conjecture of Shafarevich, which asserts that in the case X is a smooth projective variety, $\tilde{X}$ has enough global holomorphic functions to separate points up to compact ambiguity.  I will describe joint work with Brunebarbe and Tsimerman which gives a complete answer to questions (1) and (2) provided $\pi_1(X)$ admits a faithful linear representation, using techniques coming from non-abelian Hodge theory. Simonyi 101 and Remote Accessa7a99c3d46944b65a08073518d638c23
Benjamin Thomas Bakker, Institute for Advanced Study

Joint IAS/PU Arithmetic Geometry

December 15, 2025 | 3:30pm - 4:30pm
Add to calendar 12/15/2025 15:3012/15/2025 16:30Joint IAS/PU Arithmetic Geometryuse-titleTopic: Affine Schubert Varieties Are Splinters Speakers: Robert Cass, Claremont McKenna College More: https://www.ias.edu/math/events/joint-iaspu-arithmetic-geometry-34 Schubert varieties are known to be Frobenius split in positive characteristic by the work of Mehta and Ramanathan. More recently, Bhatt showed that the full flag variety for $GL_n$ is a splinter by entirely different methods. In this talk, we will explain these concepts and show how to generalize Bhatt's result to all Schubert varieties for all reductive groups. Our methods apply equally well to affine Schubert varieties, which are related to the Langlands program and to the representation theory of algebraic groups. This is joint work with João Lourenço. Simonyi 101 and Remote Accessa7a99c3d46944b65a08073518d638c23
Robert Cass, Claremont McKenna College

Joint IAS/PU Symplectic Geometry Seminar

December 16, 2025 | 1:00pm - 2:00pm
Add to calendar 12/16/2025 13:0012/16/2025 14:00Joint IAS/PU Symplectic Geometry Seminaruse-titleTopic: Cohomologous Symplectic Forms with Different Gromov Widths Speakers: Shengzhen Ning, University of Minnesota More: https://www.ias.edu/math/events/joint-iaspu-symplectic-geometry-seminar-5 For closed symplectic manifolds, the Gromov width is among the most fundamental symplectic capacities: it measures the size of the largest embedded symplectic ball and is sensitive to the perturbation of the symplectic forms. A natural question, posed as Problem 46 in McDuff-Salamon's problem list, asks whether there are cohomologous symplectic forms with different Gromov widths. In this talk, I will explain how to obtain such examples in dimension 6 from dimension 4, by adapting Ruan's early example of deformation inequivalent symplectic forms. Simonyi 101 and Remote Accessa7a99c3d46944b65a08073518d638c23
Shengzhen Ning, University of Minnesota

Joint IAS/PU Groups and Dynamics Seminar

December 16, 2025 | 4:30pm - 5:30pm
Add to calendar 12/16/2025 16:3012/16/2025 17:30Joint IAS/PU Groups and Dynamics Seminaruse-titleTopic: Partially Hyperbolic Actions of Semisimple Lie Groups Speakers: Kurt Vinhage, University of Utah More: https://www.ias.edu/math/events/joint-iaspu-groups-and-dynamics-seminar-41 Zimmer proposed the study of higher-rank semisimple group actions in the 1980's after showing certain rigidity results, especially about associated cocycles in the measurable category. In this talk, I will describe recent progress towards classifying such actions in the presence of uniformly expanding and contracting directions. Joint work with D. Damjanovic, R. Spatzier and D. Xu. Simonyi 101a7a99c3d46944b65a08073518d638c23
Kurt Vinhage, University of Utah

Special Groups and Dynamics Seminar

December 17, 2025 | 10:30am - 12:00pm
Add to calendar 12/17/2025 10:3012/17/2025 12:00Special Groups and Dynamics Seminaruse-titleTopic: Asymptotic dimension, Isoperimetric Problem, and Traveling Salesman Problem in Groups Speakers: Anna Erschler, Institute for Advanced Study More: https://www.ias.edu/math/events/special-groups-and-dynamics-seminar-0 In many groups, the optimal diameter for the solutions of the isoperimetric problem is asymptotically equivalent to the lower bound coming from their cardinality; in this situation one says that the Følner function is _lossless_ with respect to the isodiametric function. Answering a question of Nowak, we prove that for some   groups the Følner function is _not_ lossless, and we compute the asymptotics of the isodiametric function in many examples. We study the relationship between the isodiametric function, the control function for the asymptotic dimension of the group, and an invariant related to the Universal Traveling Salesman Problem. We prove that the isodiametric function is equivalent to the control function for the asymptotic dimension for a broad class of groups with a lossless Følner function. In particular, this applies to the diagonal products of Brieussel–Zheng associated with a sequence of expander graphs.  For our main examples, the Følner function is not lossless with respect to the isodiametric function; nevertheless, we show that in these examples the control function is lossless with respect to the isodiametric one. Such groups include wreath products, Hall’s nilpotent-by-abelian groups, and Lampshuffler groups. While many amenable groups of finite Assouad–Nagata dimension have a lossless control function, we also construct examples with a non-lossless control function. We also discuss open problems concerning how the isoperimetric problem influences algebraic properties of groups. We show that every amenable group of finite Assouad–Nagata dimension has Shalom’s property HFD. In particular, such groups cannot be simple and cannot be purely torsion. The first conclusion contrasts with the simple groups of Burger and Mozes, some of which are quasi…Simonyi 101 and Remote Accessa7a99c3d46944b65a08073518d638c23
Anna Erschler, Institute for Advanced Study
More Events

Now accepting nominations for the 2024 Salem Prize

Raphael Salem

The Institute for Advanced Study is accepting nominations for the 2024 Salem Prize, which, since 1968, has been awarded to young mathematicians judged to have completed outstanding work on harmonic analysis and related topics.

Nominations should include the nominee’s CV and a letter explaining the significance of their work. More information on the prize and the nomination can be found here.

Honoring the Legacy of Emmy Noether

Applications

Memberships and How to Apply
Deadline December 1

Women and Mathematics
Deadline February 16

Summer Collaborators Program
December 1

NSF

The School of Mathematics wishes to acknowledge and thank the National Science Foundation for their generous support of the School's programs each year.

Mathematics Institutes

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