Topology seminar

I will talk about a series X_k, k ≥ 0, of topological spaces whose rational homotopy type admits an action of the Lie group of exceptional type E_k. These rational homotopy types govern supergravity in (11-k)-dimensional spacetime. This extends Mysterious Duality of Iqbal, Neitzke, and Vafa (2001) as a mysterious connection between M-theories in various dimensions and del Pezzo surfaces to a triality which adds a connection to rational homotopy theory. The connection between physics and topology in our work is not mysterious but rather explicit, and if a conjectural connection between topology and algebraic geometry is clarified, it will unveil the whole mystery of the triality at once. This is based on published [arXiv:2111.14810, arXiv: 2212.13968] and ongoing work with Craig’s and mine friend Hisham Sati.

Vincent Hall 570 or  Zoom:   https://umn.zoom.us/j/95323153681?pwd=SVFzbVVwTnJnN0l0VVJJdzJ5dmVFUT09  - Meeting ID: 953 2315 3681Passcode: uWgLL9

In this talk I will discuss what is and isn't known about the homology of 3-manifolds and their finite covers. In particular, we will consider how homology can grow in towers of finite covers.

 VinH 570 or via  Zoom  - Meeting ID: 953 2315 3681 - Passcode: uWgLL9

A quandle is an algebraic structure satisfying laws like the conjugation operation in a group. In this talk I'll discuss how a knot naturally has an associated quandle, and a homotopy-theoretic interpretation of where this structure comes from. I'll also discuss an analogue of a theorem of Milnor, identifying the homotopy type of the free quandle on a topological space, and how this impacts the study of "cohomology for quandles". This is joint work with Markus Szymik.Location:   In person in VinH 570, broadcast on Zoom:   https://umn.zoom.us/j/95323153681?pwd=SVFzbVVwTnJnN0l0VVJJdzJ5dmVFUT09

The moduli spaces of smooth projective curves with marked points have cohomology that attaches characteristic classes to surface bundles with disjoint sections. As such, this cohomology is of fundamental importance in algebraic geometry and topology. However, only a tiny fraction of the cohomology is understood. I will present joint works with Bibby, Chan and Yun, and with Hainaut, in which we gain access to the least algebraic part of the cohomology for curves of genus 2, using tropical geometry and configuration spaces on graphs. In particular we find the first examples of families of cohomology classes in the top cohomological dimension, which seem to tell a geometric story that is yet to be understood.

 VinH 570, broadcast on Zoom

After introducing several ways to think about the cohomology of the moduli space of curves, I will discuss a recent theorem of mine saying that in a stable range, the rational cohomology of the moduli space of curves with level structures is the same as that of the ordinary moduli space of curves: a polynomial algebra in the Miller-Morita-Mumford classes.

 VinH 570 or via Zoom :  Meeting ID: 953 2315 3681 - Passcode: uWgLL9

In this talk I will discuss the topological structure of the space Hom(Z^n,G) of commuting n-tuples in G, where G is a unitary group or general linear group over C. I will explain how the equivariant homology of Hom(Z^n,G) is related to Hochschild homology, and how this can be used in homology calculations. In particular, I will explain how to obtain the rational homology, homology stability, and some results on p-torsion.

VinH 570, broadcast on Zoom:   https://umn.zoom.us/j/95323153681?pwd=SVFzbVVwTnJnN0l0VVJJdzJ5dmVFUT09

The homotopy groups of topological modular forms are very interesting and most computations need a lot of nontrivial topology information. In this talk, we present two new approaches of the 2-primary computation based on new techniques from equivariant homotopy theory and motivic homotopy theory respectively. The new approaches use more algebraic input and provide new information. In particular, the equivariant approach avoids the use of Toda brackets. The motivic approach settles a sign in the multiplicative structure, which is the last unresolved detail about the multiplicative structure in Bruner and Rognes' book. This talk is based on joint projects with Zhipeng Duan, Dan Isaksen, Hana Jia Kong, Yunze Lu, Yangyang Ruan, Guozhen Wang, and Heyi Zhu.

VinH 570, broadcast on Zoom:   https://umn.zoom.us/j/95323153681?pwd=SVFzbVVwTnJnN0l0VVJJdzJ5dmVFUT09

Abstract not available

Abstract not available

VH 570

Abstract not available

  In person - VinH 570, broadcast on Zoom:   https://umn.zoom.us/j/95323153681?pwd=SVFzbVVwTnJnN0l0VVJJdzJ5dmVFUT09

Abstract not available

 VinH 570 or via  Zoom :  Meeting ID: 953 2315 3681 - Passcode: uWgLL9

Abstract not available

VinH 570, broadcast on Zoom:   https://umn.zoom.us/j/95323153681?pwd=SVFzbVVwTnJnN0l0VVJJdzJ5dmVFUT09

 VinH 570, broadcast on Zoom:   https://umn.zoom.us/j/95323153681?pwd=SVFzbVVwTnJnN0l0VVJJdzJ5dmVFUT09

Abstract not available

Vincent Hall 570 - Zoom Meeting