Department of

Mathematics


Seminar Calendar
for Graduate Geometry and Topology Seminar events the year of Thursday, October 11, 2018.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, September 7, 2018

4:00 pm in Altgeld Hall 241,Friday, September 7, 2018

A generalization of pair of pants decompositions

Jesse Huang (UIUC)

Abstract: We will talk about higher dimensional pair of pants decompositions for smooth projective hypersurfaces.

Friday, September 14, 2018

4:00 pm in 241 Altgeld Hall,Friday, September 14, 2018

3 invariants of manifolds you won稚 believe are the same!

Hadrian Quan

Abstract: We値l start by discussing everyone痴 favorite invariant: the determinant of a linear map. After generalizing this to an invariant of a chain complex, we値l talk about three different different ways to get a number from a representation of $\pi_1(M)$: topological, analytic, and dynamical. Number 3 might surprise you!

Friday, September 21, 2018

4:00 pm in 241 Altgeld Hall,Friday, September 21, 2018

The geometry of some low dimensional Lie groups

Ningchuan Zhang (UIUC)

Abstract: In this talk, I'll give explicit geometric descriptions of some low dimensional matrix groups. The goal is to show $\mathrm{SU}(2)\simeq S^3$ is a double cover of $\mathrm{SO}(3)$ and $\mathrm{SL}_2(\mathbb{C})$ is a double cover of the Lorentz group $\mathrm{SO}^+(1,3)$. Only basic knowledge of linear algebra and topology is assumed.

Friday, September 28, 2018

4:00 pm in 241 Altgeld Hall,Friday, September 28, 2018

Integrability of the Toda lattice

Matej Penciak (UIUC)

Abstract: I will introduce topics such as the Toda lattice, the Lax matrices, and integrability.

Friday, October 5, 2018

4:00 pm in 241 Altgeld Hall,Friday, October 5, 2018

An introduction to Ratner's theorem

Venkata Sai Narayana Bavisetty

Abstract: This talk will be an introduction to ergodic theory. I will start out by explaining what ergodicity means and state Ratner's theorem. I will conclude by sketching the proof of Oppenheim conjecture(now a theorem).

Friday, October 12, 2018

4:00 pm in 241 Altgeld Hall,Friday, October 12, 2018

Supersymmetry and Morse theory

Lutian Zhao (UIUC)

Abstract: In 1982, Edward Witten discovered the topological invariant hidden inside the supersymmetric quantum field theory: the Morse complex can be constructed by the supersymmetric model. In this talk, I値l try to explain the construction from the very beginning assuming no knowledge of supersymmetry as well as Morse theory. If time permitted, I値l discuss some interpretation of index theorem by supersymmetry.

Friday, October 19, 2018

4:00 pm in 241 Altgeld Hall,Friday, October 19, 2018

An Introduction to Persistent Homology

Dan Carmody (UIUC)

Abstract: In this talk, I'll start by introducing the Cech and Vietoris-Rips complexes, then compute some basic examples of persistent homology using the python library Gudhi (Maria et al., 2014). I'll introduce one of the standard metric structures on the space of persistence diagrams, then end by surveying some of the applications of persistent homology to crop science and human biology.

Friday, November 2, 2018

4:00 pm in 241 Altgeld Hall,Friday, November 2, 2018

K3 surfaces and Hyperkahler manifolds

Sungwoo Nam (UIUC)

Abstract: In classification of complex surfaces, K3 surfaces take position similar to that of elliptic curves in smooth projective curves. With their higher-dimensional analogues, compact hyperkahler manifolds, they play an important role in string theory as well. In this talk, we will see their definition and basic properties, mostly about their cohomology. We値l then discuss a theorem of Matsushita and Hwang, which shows rigidity of the structure of these manifolds.

Friday, November 9, 2018

4:00 pm in 241 Altgeld Hall,Friday, November 9, 2018

Introduction to knot theory and the topology of knots

Chaeryn Lee (UIUC)

Abstract: This talk will introduce the very basic concepts and goals of knot theory. It will mainly focus on the topology of knots and how knot theory relates to 3-manifolds and surgery theory. Some topics to be covered will include Lens spaces, Heegaard splittings, Dehn surgery and knot exterior as a knot invariant.

Friday, November 30, 2018

4:00 pm in 241 Altgeld Hall,Friday, November 30, 2018

Counting curves in the plane

Nachiketa Adhikari (UIUC)

Abstract: There is a unique line through two points in the plane. There is a unique conic through five points (in general position). There are twelve cubics through 8 such points. So: is there a general formula for the number $N_d$ of degree d curves passing through 3d-1 points in the plane? In the 1990s, an astonishing relationship between invariants obtained in string theory and certain spaces of curves was discovered. Using these, Kontsevich obtained a recurrence formula for $N_d$. I will sketch a few of the (mathematical) ideas. This talk should be accessible to beginning graduate students.

Friday, December 7, 2018

4:00 pm in 241 Altgeld Hall,Friday, December 7, 2018

Topological K-theory and the Hopf Invariant One Problem

Elizabeth Tatum (UIUC)

Abstract: I'll define topological k-theory and discuss its application to the Hopf invariant one problem.