Time : Tuesdays 12.30 to 1.30pm
Location : Hill 701 (Graduate Student Lounge)
Sep 13
Speaker : Soham Chanda
Title : Morse Flow category
Abstract : I will talk about Flow Categories, how they arise from a Morse-Smale functions and then explain one result about obtaining topological data from a Morse flow category from the Abouzaid-Blumberg paper. If I have time, I will quickly talk about Spectra and how it gives rise to "extraordinary cohomology" theories.
Sep 20
Speaker : Liuwei Gong
Title : Fake singularities
Abstract : We will define and compute what Schwarzschild metric is, find out "fake" singularities caused by choice of coordinates and discuss similar phenomenon happening in other metrics.
Sep 27
Speaker : Sriram Raghunath
Title : Knotty hyperbolic tetrahedra!
Abstract : In this talk we will explore connections between hyperbolic geometry, topology of 3-manifolds and knot invariants. Come if you want to hear more about geometrization, Jones polynomials, hyperbolic volumes and the volume conjecture.
Oct 4
Speaker : Joy Hamlin
Title : The Evenly Spaced Integer Topology
Abstract : You can prove that there are infinitely many primes by putting a nonstandard topology on the integers! I wanted to learn more about the properties of this topology and I needed a topic to talk about at this seminar. Come by if you want to hear me say the word clopen a lot, or if you have strong objections to me saying the word clopen.
Oct 11
Speaker : Bernardo Do Prado Rivas
Title : Conley Index Theory
Abstract : The idea is to have a crash course in dynamics from ordinary differential equations. I will talk a bit about general results, invariant sets, and Conley's key ideas to understand them. We might have some hand-waving and proofs by drawing, but we will easily compute the index of strange attractors.
Oct 18
Speaker : Devin Bristow
Title :: TBD
Abstract : TBD
Archival Schedule
Spring 2022
Past Seminars
Feb 8
Speaker : Soham Chanda
Title : Morse Homology
Abstract : In this talk we'd go over classical morse theory in the first half and then proceed to construct morse homology chain complex from moduli space of negative gradient flows.
Feb 15
Speaker : Aakash Parikh
Title : Spectral sequences
Abstract : In this talk we will define the spectral sequence of a double complex and give some examples of computations using the Serre spectral sequence for homology
Feb 22
Speaker : Sriram Raghunath
Title : Various constructions of the Poincare homology sphere
Abstract : We have all heard about the Poincare conjecture – every compact simply connected 3-manifold without boundary is homeomorphic to the 3-sphere. But Poincare initially thought that any 3-manifold which has all its homology groups isomorphic to those of S3 should be homeomorphic to S3. This turned out to be spectacularly wrong – there are in fact infinitely many counterexamples to this statement. In fact, Poincare himself came up with the most famous counterexample of all – the Poincare homology sphere. In this talk, we will discuss multiple constructions of this space from different points of view – this is an excuse for me to talk about interesting techniques in low dimensional topology.
March 1
Speaker : Dong Yeong Ko
Title : Geometric Variational problems related to mean curvature
Abstract : In this talk, we introduce geometric variational problems related to mean curvature. We cover the notion of geodesics, minimal hypersurfaces and their constant mean curvature analog as a critical point of area functional and its generalization. Moreover, if time permits, we will discuss the Morse theory of geodesics and minimal hypersurfaces, and recent progress on this variational theory on its spatial distibutions.
March 8
Speaker : Ishaan Shah
Title : Topological Quantum Field Theory
Abstract : Topological Quantum field theories (TQFTs) are highly symmetric QUantum Field Theories allowing for exact solutions. In this talk we classify 2D TQFTs and potentially look at 2D CFTs or higher dimensional TQFTs.
March 15 : Spring Break!
March 22
Speaker : Sumeet Khandelwal
Title :: Stacks and moduli spaces
Abstract : In this talk we will look at stacks. Stacks is a structure that can be used to extend the notion of moduli spaces when objects have non trivial automorphism group and are an analog of orbifolds. In this talk we will primarily look at the space of triangles and how it can be modelled using a stack. We will then see some other examples of stacks.
March 29
Speaker : Brian Pinsky
Title : Branch Groups
Abstract : Like many areas of group theory, the study of branch groups began with burnside’s problem: whether every finitely generated torsion group is finite. One of the first counterexamples was Grigorchuck’s group, a group of self-similar automorphisms of cantor space. Self similarity is a powerful tool for working with these groups, and they are among the most useful examples in geometric group theory. I will illustrate this technique by proving Grigorchuck’s group is torsion, this is very elegant and requires no group theory background. Afterwards, I’d like to go over a generalization of Grigorchuck’s construction using coding theory; one I thought I’d invented, but Zoron Sunic actually beat me by 15 years. I’d also like to talk about generalizations acting on infinite type surfaces, rather than cantor space, as according to my enthusiastic office-neighbor and some papers I still need to read, this is fruitful.
April 12
Speaker : Soham Chanda
Title : Floer homology and Neck-stretching
Abstract : In this talk we will begin with basics of lagrangian intersection floer homology and then proceed to talk about compactification of holomorphic maps under neck-stretching.
April 26
Speaker : Aakash Parikh
Title :Basics of handle decompositions and handle calculus
Abstract : In this talk we will define what a handle is, describe the Morse theoretic result that smooth compact manifolds admit handle decompositions, give some examples of such decompositions, and (time permitting) discuss some particulars of the 3 and 4 dimensional cases.