**Problem of the Week**

**BUGCAT**

**Zassenhaus Conference**

**Hilton Memorial Lecture**

**BingAWM**

**Math Club**

seminars:topsem

We meet **Thursdays** at **2:50–3:50 pm** in **Whitney Hall 100E**. This semester's organizer is Cary Malkiewich. The seminar has an announcement mailing list open to all.

Topics include: geometric group theory, differential geometry and topology, low-dimensional topology, algebraic topology, and homotopy theory.

**August 31st**

No seminar this week

**September 7th**

No seminar this week (cancellation)

**September 14th**

Speaker:**John Rached**(Binghamton)

Title:**Quantitative behavior of horocycle flow on the moduli space of genus 2 surfaces***Abstract:*The action of SL(2,R) on moduli space exhibits measure rigidity, analogously to Ratner’s theorems for unipotent flows on homogeneous spaces, due to the seminal work of Eskin-Mirzakhani. Similar results cannot hold for the horocycle flow on moduli space, but for special subvarieties of strata (eigenform loci), some key tools from homogeneous dynamics have an incarnation in this inhomogeneous setting. A version of Ratner’s theorem holds for eigenform loci, and a flurry of recent work on quantitative results for actions on homogeneous spaces begs a natural question - can one effectivize arguments for the horocycle flow on eigenform loci? We give some support for a positive answer to this question, and make some conjectures.

**September 21st**

No seminar this week (cancellation)

**September 28th**

Speaker:**Maxine Calle**(University of Pennsylvania)

Title:**Nested cobordisms and TQFTs***Abstract:*The folk theorem identifying 2-dimensional TFQTs with Frobenius algebras is a starting point for a lot of interesting mathematics, from mathematical physics to homotopy theory to higher category theory. In this talk, we will explore what happens if we replace the cobordism category with a category of nested cobordisms, where 2-dimensional surfaces may have embedded 1-dimensional submanifolds, and what kind of algebraic structure the corresponding nested TQFTs pick out. This is based on ongoing work joint with R. Hoekzema, L. Murray, N. Pacheco-Tallaj, C. Rovi, and S. Sridhar.

**October 5th**

Speaker:**Cary Malkiewich**(Binghamton)

Title:**Higher scissors congruence***Abstract:*Hilbert's Third Problem asks for sufficient conditions that determine when two polyhedra in three-dimensional Euclidean space are scissors congruent. Classically, the attempts to solve this problem (in this and other geometries) lead into group homology and algebraic K-theory, in a somewhat ad-hoc way. In the last decade, Zakharevich has shown that the presence of K-theory here is not ad-hoc, but is integral to the definition of scissors congruence itself. This leads to a natural notion of higher scissors congruence groups, in which the 0th group is the classical one that determines the answer to Hilbert's Third Problem.In this talk, I'll describe a surprising recent result that these higher groups arise from a Thom spectrum. Its base space is the homotopy orbit space of a Tits complex, and the vector bundle is the negative tangent bundle of the underlying geometry. Using this result, we can explicitly compute the higher scissors congruence groups for the one-dimensional geometries, and give exact sequences that express them for the two-dimensional geometries. Much of this is joint work with Anna-Marie Bohmann, Teena Gerhardt, Mona Merling, and Inna Zakharevich.

**October 12th**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**October 19th**

No seminar this week (Fall break)

**October 26th**

Speaker:**Brenda Johnson**(Union College)

Title:**TBA***Abstract:*TBA

**November 2nd**

Speaker:**Paul Apisa**(University of Wisconsin)

Title:**Hurwitz Spaces, Hecke Actions, and Orbit Closures in Moduli Space***Abstract:*The moduli space of Riemann surfaces is a space whose points correspond to the ways to endow a surface with a hyperbolic metric or, equivalently, complex structure. Geodesic flow on moduli space can be used to generate an action of GL(2, R) on its cotangent bundle. While work of Eskin, Mirzakhani, Mohammadi, and Filip implies that GL(2, R) orbit closures are varieties, the question of which ones occur is wide open. Aside from two well-understood constructions (taking loci of branched covers and subloci of rank two orbit closures) there are only 3 known families of orbit closures: the Bouw-Moller curves, the Eskin-McMullen-Mukamel-Wright (EMMW) examples, and 2 sporadic examples. Building on ideas of Delecroix-Rueth-Wright, I will describe work showing that the Bouw-Moller and EMMW examples can be constructed using just the representation theory of finite groups. The main idea is to connect these examples to Hurwitz spaces of G-regular covers of the sphere for an appropriate finite group G. In the end, I will describe a construction that inputs a finite group G and a set of generators satisfying a combinatorial condition and outputs a GL(2, R) orbit closure in moduli space.

**November 9th**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**November 16th**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**November 23rd**

No seminar this week (Thanksgiving)

**November 30th**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**December 7th**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**January 18th**

Organizational meeting

**January 25th**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**February 1st**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**February 8th**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**February 15th**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**February 22nd**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**February 29th**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**March 7th**

No seminar this week (spring break)

**March 14th**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**March 21st**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**March 28th**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**April 4th**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**April 11th**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**April 18th**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**April 25th**

No seminar this week (Tuesday classes meet)

**May 2nd**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

seminars/topsem.txt · Last modified: 2023/10/02 20:16 by malkiewich

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