One of the most well-known examples of a cluster structure comes from Penner's lambda-length coordinates on the decorated Teichmuller space of a surface. In 2019, Penner and Zeitlin defined a super-manifold generalizing the decorated Teichmuller space, which involves new anti-commuting variables. I wall talk about some recent work with Gregg Musiker and Sylvester Zhang, where we showed that the coordinates on the decorated super Teichmuller space have many of the nice properties associated to a cluster structure, such as a kind of Laurent phenomenon, positivity, and some interesting combinatorial interpretations of the Laurent expressions, involving double dimer covers of certain graphs.

In this talk, we give an overview of some basic properties of wavelets. We then introduce the Windowed Scattering Transform and go over stability and invariance properties that make it desirable as a feature extractor. Finally, we provide a generalization of the Windowed Scattering Transform that is translation invariant and discuss other stability and invariance properties of our generalized Scattering Transform.
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This will be a hybrid seminar and take place in C117 Wells Hall and via Zoom at https://msu.zoom.us/j/99426648081?pwd=ZEljM3BPUXg2MjVUMVM5TnlzK2NQZz09 .

Mathematics education research is overwhelmingly assimilationist in its desire
to change people, teachers, students, researchers, instead of changing the mathematics. In this teaching-research collaboration, one teacher (Tina Haselius), two graduate research assistants (Sofía Abreu and Melvin Peralta), and one mathematics education researcher (Higinio Dominguez) will share their emerging experiences learning how to animate mathematical concepts. While one key goal in our collaboration has been to resist the violence of trying to change, assimilate, and colonize learners, the process of animating mathematical concepts has, in beautiful and nonviolent ways, allowed us to experience change in and among ourselves as we learn to (co)respond to the animacy and agency of the mathematical concepts that we set out to animate in our teaching-research group.

The birational automorphism group is a natural birational invariant associated to an algebraic variety. In this talk, we study the specialization homomorphism for the birational automorphism group. As an application, building on work of Kollár and of Chen–Stapleton, we show that a very general n-dimensional complex hypersurface X of degree ≥ 5⌈(n+3)/6⌉ has no finite order birational automorphisms. This work is joint with Nathan Chen and David Stapleton.

In operator algebras, specifically free probability, free transport is a technique for producing state-preserving isomorphisms between C* and von Neumann algebras that was developed by Guionnet and Shlyakhtenko in their 2014 Inventiones paper. The inspiration for their work comes from the field of optimal transport, specifically work of Brenier from 1991 who showed that under very mild assumptions one can push forward a probability measure on $\mathbb{R}^n$ to the Gaussian measure. In the non-commutative case, Guionnet and Shlyakhtenko showed that if $x_1,\ldots, x_n$ are self-adjoint operators in a tracial von Neumann algebra $(M,\tau)$ whose distribution satisfies an "integration-by-parts" formula up to a small perturbation, then these operators generate a copy of the free group factor $L(\mathbb{F}_n)$. In this series of talks, I will give an overview of their proof, discuss some applications of their result, and survey the current state of free transport theory.

In this talk I will detail a construction of symmetric link
homology. In particular, this provides a non-trivial categorification of
1 and a finite dimensional categorification of the colored Jones
polynomial and a new categorification of the Alexander polynomial. I
will also explain how this relates to the triply graded homology and
knot Floer homology.

In joint work with Russ Woodroofe, we showed that the order complex of the poset of all cosets of all proper subgroups of a finite group, ordered by inclusion, has noncontractible order complex using Smith Theory. A key part of our proof involves invariable generation of finite groups: two subsets $S,T$ of a group $G$ generate $G$ invariably if, for every $g,h \in G$, $g^{-1}Sg$ and $h^{-1}Th$ together generate $G$. It remains open whether the alternating group $A_n$ can be generated invariably by $\{s\}$ and $\{t\}$ with both $s,t$ having prime power order. This question is closely related to a (still open) question about prime divisors of binomial coefficients. I will discuss all of this, along with current work joint with Bob Guralnick and Russ Woodroofe about invariable generation of arbitrary simple groups by two elements of prime or prime power order.

The damped wave equation models the behavior of vibrating systems exposed to some damping force, which causes the total energy to decay. In this talk, I will discuss classical results that give upper and lower bounds on decay, based on the dynamics of the geodesic flow and the support of the damping. I will discuss recent generalizations of these results to time dependent, unbounded, or anisotropic damping.
(Note location: this talk will be held in C517 due to hiring meeting in C304.)