Department of

# Mathematics

Seminar Calendar
for Graduate Geometry and Topology Seminar events the year of Friday, November 9, 2018.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     October 2018          November 2018          December 2018
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5  6                1  2  3                      1
7  8  9 10 11 12 13    4  5  6  7  8  9 10    2  3  4  5  6  7  8
14 15 16 17 18 19 20   11 12 13 14 15 16 17    9 10 11 12 13 14 15
21 22 23 24 25 26 27   18 19 20 21 22 23 24   16 17 18 19 20 21 22
28 29 30 31            25 26 27 28 29 30      23 24 25 26 27 28 29
30 31


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’t believe are the same!

Abstract: We’ll start by discussing everyone’s favorite invariant: the determinant of a linear map. After generalizing this to an invariant of a chain complex, we’ll 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’ll try to explain the construction from the very beginning assuming no knowledge of supersymmetry as well as Morse theory. If time permitted, I’ll 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’ll 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.