Department of

# Mathematics

Seminar Calendar
for Graduate Student Algebraic Geometry Seminar events the year of Thursday, October 11, 2018.

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events for the
events containing

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


Tuesday, January 16, 2018

4:00 pm in Illini Hall 1,Tuesday, January 16, 2018

#### Organizational meeting

Abstract: We'll have a cookies party while deciding what'll be in the seminar this semester.

Tuesday, January 23, 2018

4:00 pm in Illini Hall 1,Tuesday, January 23, 2018

#### Moduli space of compact Riemann surfaces

###### Jin Hyung To (UIUC)

Abstract: We will overview the moduli space of compact Riemann surfaces.

Tuesday, January 30, 2018

4:00 pm in Illini Hall 1,Tuesday, January 30, 2018

#### Riemann-Roch Formula and The Dimension of Our Universe

###### Lutian Zhao   [email] (UIUC)

Abstract: In this talk we'll introduce the classical Riemann-Roch formula, which appears as a vast generalization of the Euler-Maclaurin formula for the integrals. As an interesting application, the critical dimension for the bosonic string theory can be calculated by these formula to be d=26, which matches with the physical prediction using light-cone quantization. No basic knowledge on string theory and Riemann-Roch will be assumed.

Tuesday, February 6, 2018

4:00 pmTuesday, February 6, 2018

#### Cancelled

Abstract: Cancelled

Tuesday, February 13, 2018

4:00 pm in Illini Hall 1,Tuesday, February 13, 2018

#### Introduction to Cohomological Field Theory

###### Sungwoo Nam (UIUC)

Abstract: Cohomological field theory(CohFT) was first introduced by Kontsevich and Manin to organize the data of Gromov-Witten theory and quantum cohomology into a list of axioms. Although its main model is Gromov-Witten theory, it has been also successful dealing with problems outside of Gromov-Witten theory. In this talk, I will introduce the notion of CohFT, Givental-Teleman’s classification of semisimple CohFTs and some concrete examples. Basic knowledge of Gromov-Witten theory will be helpful, but it is not assumed in this talk.

Tuesday, February 20, 2018

4:00 pm in Illini Hall 1,Tuesday, February 20, 2018

#### A Bird's-Eye View of Seiberg Witten Integrable Systems

###### Matej Penciak (UIUC)

Abstract: In this talk I will give a rudimentary description of supersymmetric gauge theories, and focus on the particular case of $N=2$ supersymmetry in dimension $4$ with gauge group $SU(2)$. In this setting, originally noticed and explained by Seiberg and Witten in 1994, the moduli of vacua exhibits the structure of an algebraic integrable system. I will explain how this structure manifests itself, and the give a sketch of the calculation that Seiberg and Witten made in their original paper. If time permits, I will explain the generalization of this story to more general gauge groups, and with possible additional matter fields included in the theory.

Tuesday, February 27, 2018

4:00 pm in 1 Illini Hall,Tuesday, February 27, 2018

#### Introduction to GIT

###### Itziar Ochoa de Alaiza Gracia (UIUC)

Abstract: The aim of this talk is to give the motivation for the GIT quotient. We will do so by introducing different notions of quotients, illustrated by examples. Finally we will define the Affine and projective GIT quotients.

Tuesday, March 6, 2018

4:00 pm in 1 Illini Hall,Tuesday, March 6, 2018

#### Introduction to GIT, II

###### Itziar Ochoa de Alaiza Gracia

Abstract: The aim of this talk is to give the motivation for the GIT quotient. We will do so by introducing different notions of quotients, illustrated by examples. Finally we will define the Affine and projective GIT quotients.

Tuesday, March 13, 2018

4:00 pm in 1 Illini Hall,Tuesday, March 13, 2018

#### Algebraic Morse theory from GIT

###### Jesse Huang (UIUC)

Abstract: Birational geometry is closely tied to GIT quotients and variations. In this episode of GIT series, I will apply the machinery to a countable set of basic examples, through which we shall see how the change of linearization produces elementary birational transformations.

Tuesday, April 10, 2018

4:00 pm in 1 Illini Hall,Tuesday, April 10, 2018

#### GIT quotients of flag varieties

###### Joshua Wen (UIUC)

Abstract: As we’ve seen, GIT quotients depend on a choice of line equivariant line bundle, and varying this choice can lead to drastic or subtle changes between quotients. After introducing a framework for ‘variation of GIT’ by Dolgachev and Hu, I want to consider a case of the flag variety and its action either by a torus or semisimple group. Here, one already knows many equivariant line bundles, and studying dimensions of invariant sections leads to results of representation-theoretic significance.

Tuesday, April 24, 2018

4:00 pm in 1 Illini Hall,Tuesday, April 24, 2018

#### Moduli of Twisted Curve

###### Hao Sun (UIUC)

Abstract: I'll give an introductory talk about the twisted curves. Twisted curves are related to the study of r-spin Witten classes and r-spin geometry of the moduli space of curves.

Wednesday, August 29, 2018

4:00 pm in 2 Illini Hall,Wednesday, August 29, 2018

#### Organizational Meeting

Wednesday, September 5, 2018

4:00 pm in 2 Illini Hall,Wednesday, September 5, 2018

#### (Crystalline) differential operators in positive characteristic

###### Shiyu Shen (UIUC Math)

Abstract: I will talk about several features of (Crystalline) differential operators in characteristic $p$, including the Azumaya property and two theorems by Cartier.

Wednesday, September 12, 2018

4:00 pm in 2 Illini Hall,Wednesday, September 12, 2018

#### Differential Equations from Hodge Theory

###### Lutian Zhao   [email] (UIUC Math)

Abstract: The classical theory of elliptic integrals is the milestone in the history of various fields in math: algebraic geometry, differential equations, number theory,.. etc. In this talk, I'll use this as the motivating example for the theory of periods. I'll talk about how we get some equations for the periods and interpret these equations in terms of Hodge theory. As an interesting application, I'll calculate the number of rational curves on quintic threefold by these differential equations. Only complex analysis is assumed.

Wednesday, September 19, 2018

4:00 pm in 2 Illini Hall,Wednesday, September 19, 2018

#### Window equivalences and spherical functors

###### Jesse Huang   [email] (UIUC Math)

Abstract: We will appreciate some recent results on the derived categories of GIT quotients through the basic example of a flip/flop.

Wednesday, September 26, 2018

4:00 pm in 2 Illini Hall,Wednesday, September 26, 2018

#### Line bundles on abelian varieties

###### Matej Penciak   [email] (UIUC Math)

Abstract: In this talk I want to give classical results on line bundles on abelian varieties. I’ll begin with the Appel-Humbert theorem. Then I will give an introduction to theta functions and show that they can be identified with sections of line bundles. This will connect the older approach with the more well-known description in terms of divisors. Finally, I’ll consider more general problem of classifying vector bundles on elliptic curves, and describe Atiyah’s solution to the classification problem.

Wednesday, October 3, 2018

4:00 pm in 2 Illini Hall,Wednesday, October 3, 2018

#### Flops and derived categories of threefolds, Part 1

###### Sungwoo Nam (UIUC Math)

Abstract: In his paper, Bridgeland showed that derived categories of threefolds, which are related by flopping operations, are equivalent. Besides its own interest, this result can be used to study behavior of invariants of threefolds under birational morphisms. In this talk, we will present Bridgeland's work for two weeks. As the main idea involves constructing flop as a moduli space of perverse point sheaves, I'll introduce some notions such as derived categories and t-structures and their properties relevant to the proof. After that, I will give application of the theorem on birational Calabi-Yau threefolds and curve counting invariants.

Wednesday, October 10, 2018

4:00 pm in 2 Illini Hall,Wednesday, October 10, 2018

#### Flops and derived categories of threefolds, part 2

###### Ciaran O'Neill (UIUC Math)

Abstract: We will give the proof of Bridgelands theorem, stated last time. We will introduce Fourier-Mukai transforms, an important part of the proof.

Wednesday, October 17, 2018

4:00 pm in 2 Illini Hall,Wednesday, October 17, 2018

Abstract: TBD