in this talk we'll investigate the primeness of generalized wreath product ii1 factors using techniques from deformation/rigidity theory. we give general conditions relating tensor decompositions of generalized wreath products to stabilizers of the associated group action, and use this to find new examples of prime ii1 factors.

in this talk, i will give a survey of recent and upcoming results on various linear, semilinear, and quasilinear wave equations on a wide class of dynamical spacetimes in various even and odd spatial dimensions. these results include asymptotics for a wide range of nonlinearities. for many of these results, the spacetimes under consideration have only weak asymptotic flatness conditions and are allowed to be large perturbations of the minkowski spacetime, provided that an integrated local energy decay estimate holds. we explain the dichotomy between even- and odd-dimensional wave behaviour. part of this work is joint with mihai tohaneanu and jared wunsch.

configuration spaces are not only fundamental objects in mathematics, but appear in numerous areas such as robot motion planning, dna sequencing, sensor networks, and origami designs. our story is motivated by objects in algebraic geometry, namely the configuration space of surface deformations. to understand this space, we consider a combinatorial viewpoint based on scribbling loops on the surface. this leads to a classification of such spaces that can be realized as convex polytopes, capturing elegant hidden algebraic
structures.  these spaces now appear across a broad spectrum of research, including amplituhedra, geometric group theory, and phylogenetics networks. the entire talk is heavily infused with visual imagery and concrete examples.

topological hochschild homology(thh), which is a lift of hochschild homology to the stable category, has recently seen a large paradigm shift in the way it and related invariants are studied.
this is due to several groundbreaking results, among which are the results of bhatt, morrow, and scholze which introduce the quasisyntomic topology and compute the quasisyntomic filtration of topological hochschild homology, topological negative cyclic homology ($tc^{-}$), topological periodic homology(tp), and topological cyclic homology(tc). building on these results, i will talk about the quasisyntomic filtration on the quasisyntomic sheaves $thh(-)^{hc_n}$ and $thh(-)^{tc_n}$ where $c_n$ is the finite cyclic group of order $n$. these give cohomology theories that interpolate between the quasisyntomic filtrations on $thh$ and those on $tc^{-}$ and $tp$, and as it turns out can be expressed in terms of sheaves already of central importance to the study of the cohomology theories introduced by bhatt, morrow, and scholze.
as applications, i will explain how these filtrations can be used to extend the results of angeltveit, gerhardt, and hesselholt on the k-theory of truncated polynomial algebras, and a result on topological restriction homology.

i'm gonna introduce p-adic analysis and i'm gonna talk about the skolem-mahler-lech theorem and i'm gonna blow your mind.

the fractal uncertainty principle (fup) was introduced by dyatlov and zahl which states that a function cannot be localized near a fractal set in both position and frequency spaces. it has rich applications in spectral gaps and quantum chaos on hyperbolic manifolds and has recently been an active area of research in harmonic analysis. i will talk about the history of the fractal uncertainty principle and explain its applications to spectral gaps. then i will talk about our recent work, joint with aidan backus and james leng, which proves a general fractal uncertainty principle for small fractal sets, improving the volume bound in higher dimensions. this generalizes the work of dyatlov--jin using dolgopyat's method. as an application, we give effective essential spectral gaps for convex cocompact hyperbolic manifolds in higher dimensions with zariski dense fundamental groups.

this talk is an exposition on the partial progress of yau's conjecture on the lower estimate of the first eigenvalue of embedded minimal hypersurfaces in a unit sphere.

in this talk we investigate stochastic chemical reaction networks with scaling methods. this approach is used to study the stability properties of the associated markov processes, but also to investigate the transient behavior of these networks. it may give insight on the impact of complex features of these networks such as their polynomial rates, leading to the coexistence of multiple timescales. several examples are discussed.

please contact professor williams for zoom information.

 a guiding question in number theory, specifically in arithmetic statistics, is counting number fields of fixed degree and galois group as their discriminants grow to infinity.  we will discuss the history of this question and take a closer look at the story in the case of quartic fields. in joint work with florea, serrano lopez, and varma, we extend and make explicit the counts of extensions of an arbitrary number field that was done over the rationals by cohen, diaz y diaz, and olivier.

rochelle gutiérrez defines four dimensions of equity in mathematics education: access, achievement, identity, and power. in this talk, we briefly explore these dimensions and specific examples of how they can motivate course design choices. in particular, i will discuss my redesign of uw-madison's college algebra course from 2016 to 2018 and course design choices for ucsd's math 2 in winter 2022.

recall that an algebraic variety is rational if it is birational to a projective space. in this talk, i will review classical results and i will report on progress in the last decade. this includes rationality of hypersurfaces,  deformation properties, and equivariant properties.