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09-27-2022 Clone: School of Mathematics

Events and Activities

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

What is...?

December 17, 2025 | 12:45pm - 1:45pm
Add to calendar 12/17/2025 12:4512/17/2025 13:45What is...?use-titleTopic: What is String Topology? Speakers: Yash Deshmukh, Institute for Advanced Study More: https://www.ias.edu/math/events/what-54 Given two families of loops on a closed smooth manifold, one can concatenate the loops at the intersections points of these families to obtain a new family of loops. This is the Chas–Sullivan product on the homology of the free loop space of a smooth manifold.  This construction can be vastly generalized to a 2D topological field theory structure consisting of operations defined using chord diagrams/fat graphs that record complicated patterns in which families of loops are cut and concatenated with each other.  These operations have applications to a wide array of questions related to geodesics, smooth topology, and symplectic topology of cotangent bundles. After some historical motivation, I will try to compute some toy examples of these operations, and indicate how they connect to some of the applications. If time permits, I will discuss briefly some exciting recent developments related to the application of the Goresky–Hingston string coproduct to smooth topology.   Simonyi 101 and Remote Accessa7a99c3d46944b65a08073518d638c23
Yash Deshmukh, Institute for Advanced Study

Joint IAS/PU Number Theory

December 18, 2025 | 3:30pm - 4:30pm
Add to calendar 12/18/2025 15:3012/18/2025 16:30Joint IAS/PU Number Theoryuse-titleTopic: Euler Systems in the Twisted Friedberg-Jacquet Setting Speakers: Shilin Lai Affiliation: University of Michigan More: https://www.ias.edu/math/events/joint-iaspu-number-theory-5 We construct the tame part of a split anticyclotomic Euler system in a setting where local multiplicity one does not hold. Instead of the traditional zeta integral approach, we prove the existence of the necessary test vectors using a new method based on the unramified Plancherel formula. This is joint work with Li Cai and Yangyu Fan. Simonyi 101 and Remote Accessa7a99c3d46944b65a08073518d638c23
Shilin Lai
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Deadline December 1

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Deadline February 16

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December 1

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