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Justin Fus, University of ��ݮ��Ƶ

The KKS Form and Symplectic Geometry of Coadjoint Orbits

A compact Lie group acts on its Lie algebra dual via the coadjoint representation. In this talk, we will explore how the coadjoint orbits of this representation carry a natural symplectic structure called the Kirillov-Kostant-Souriau (KKS) form. The KKS form is preserved by the action. If time permits, we will show that there is a moment map for the action that coincides with the inclusion map of the orbit. A worked example for SU(2) will be performed.

MC 5403

Facundo Camano, University of ��ݮ��Ƶ

Convergence Results for Taub-NUT and Eguchi-Hanson spaces

We define multi-Taub-NUT and multi-Eguchi-Hanson spaces and look at Gromov-Hausdorff convergences involving these spaces.

MC 5403

Jiahui Huang, University of ��ݮ��Ƶ

Motivic integration for schemes, DM stacks, and Artin stacks.

We give an overview of motivic integration and its generalization to stacks. Early motivations for motivic integration involve singularity theory and the monodromy conjecture. We will explain how the change of variable formula works, and how it generalizes to the stack case. Motivic integration for stacks will use twisted or warped arcs, and we shall give a summary of the construction of the twisted arc space for DM stacks.

MC 5403

Cy Maor, Hebrew University of Jerusalem

Stability of isometric immersions and applications

An isometric immersion f:M→N between two Riemannian manifolds of the same dimension is very rigid—the values of f(p) and Df(p) at one point p∈M completely determine f. But what can be said about maps that are "almost" isometries (in a precise sense)—must they be close to true isometries? In this talk, I will survey this question from its origins in the 1960s to recent developments, and discuss its applications to non-Euclidean elasticity, where one seeks the “most isometric” immersion even when exact isometric immersions do not exist. Based on joint works with Raz Kupferman.

MC 5417

Joey Lakerdas-Gayle, University of ��ݮ��Ƶ

Effective Algebra 1

We will begin learning about recursive groups following Chapter 8 of Yuri Manin's "A Course in Mathematical Logic for Mathematicians".

MC 5417

AJ Fong, University of ��ݮ��Ƶ

The Markov equation and birational geometry

We will briefly talk about the basics on the Markov equation and its solutions, and producing Hirzebruch--Jung continued fractions from their weights. We will also describe some connections to certain degenerations of the complex projective plane. This talk is based on work of Urzúa and Zúñiga.

MC 5417

Faisal Romshoo, University of ��ݮ��Ƶ

Symmetry groups, moment maps and cohomogeneity one special Lagrangians in C^m

We will discuss the relationship between symmetries and moment maps as explained in arXiv:math/0008021 and how this allows us to construct cohomogeneity one special Lagrangians in C^m. Time permitting, we will discuss some examples of SL m-folds in C^m.

MC 5403

Alex Pawelko, University of ��ݮ��Ƶ

The Formal Kaehler Structure of the G2 Knot Space

We will explore the usual suspects of the moduli space of knots embeddable in a G2 manifold, based upon the work of Brylinski for the analogous space corresponding to the 3-dimensional cross product. This gives an infinite-dimensional "formally Kaehler" manifold, which one can consider Kaehler reduction on. If time permits, we will gesture vaguely at considerations from gauge theory and geometric quantization that motivate many interesting questions in the case of G2 manifolds.

MC 5403

Francisco Villacis, University of ��ݮ��Ƶ

A Deep Dive into Mathematicians’ Questionable Outfits

Being able to prove the most impressive theorems and having a good sense of fashion need not be mutually exclusive - except it might be? This will be up to you to judge in this talk. Together, we’ll apply the most unscientific of methodologies to create a tier list of mathematicians based solely on their dressing style - from Euclid’s timeless toga to Grothendieck’s "I’ve been living in a forest for five years" aesthetic. Be sure to bring your best outfits, otherwise you might end up in a bored grad student's tier list one day.

MC 5479

(snacks from 4:00pm)