Department of

# Mathematics

Seminar Calendar
for Algebraic geometry seminar events the year of Thursday, July 2, 2020.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      June 2020              July 2020             August 2020
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  4                      1
7  8  9 10 11 12 13    5  6  7  8  9 10 11    2  3  4  5  6  7  8
14 15 16 17 18 19 20   12 13 14 15 16 17 18    9 10 11 12 13 14 15
21 22 23 24 25 26 27   19 20 21 22 23 24 25   16 17 18 19 20 21 22
28 29 30               26 27 28 29 30 31      23 24 25 26 27 28 29
30 31


Wednesday, January 22, 2020

2:00 pm in 447 Altgeld Hall,Wednesday, January 22, 2020

#### Organizational Meeting

###### Sungwoo Nam (Illinois Math)

Abstract: We will have an organizational meeting for this semester. This involves making a plan for this semester and possibly choose a topic for a reading seminar. If you want to speak this semester, or are interested in a reading seminar, please join us and make a suggestion.

Tuesday, February 4, 2020

1:00 pm in Altgeld Hall,Tuesday, February 4, 2020

#### To Be Announced

Monday, February 10, 2020

3:00 pm in 243 Altgeld Hall,Monday, February 10, 2020

#### The moduli space of objects in the Fukaya category

###### James Pascaleff (Illinois)

Abstract: In this talk I will survey some tools from derived algebraic geometry that, when applied to Fukaya categories have applications to symplectic topology and mirror symmetry. (Note: this talk is connected with the talk I gave last week in the algebraic geometry seminar, but will be self-contained and largely disjoint.)

Wednesday, February 26, 2020

2:00 pm in 447 Altgeld Hall,Wednesday, February 26, 2020

#### Introduction to moduli spaces of sheaves

###### Sungwoo Nam (Illinois Math)

Abstract: This talk will be an introduction to moduli spaces of sheaves. We will see some motivating questions that lead to the study of moduli spaces of sheaves, and discuss examples telling us why the notion of stability is needed, even in the simplest case of vector bundles on curves. Then I will survey some results on moduli spaces of sheaves on surfaces, especially those of K3 and abelian surfaces and applications to holomorphic symplectic geometry.

Tuesday, March 3, 2020

3:00 pm in 243 Altgeld Hall,Tuesday, March 3, 2020

#### Equivariant elliptic cohomology and 2-dimensional supersymmetric gauge theory

###### Dan Berwick-Evans (UIUC)

Abstract: Elliptic cohomology can be viewed as a natural generalization of ordinary cohomology and K-theory. However, in contrast to our robust geometric understanding of cohomology and K-theory classes, we do not know of any such description for elliptic cohomology classes. A long-standing conjecture looks to provide such a geometric description using 2-dimensional supersymmetric field theory. I will describe a step forward in this program that relates equivariant elliptic cohomology over the complex numbers to certain supersymmetric gauge theories. This both refines the pre-existing program and sheds light on certain aspects, e.g., the emergence of formal group laws in the language of field theories. I will assume no prior knowledge of either elliptic cohomology or supersymmetric field theory. This is joint work with Arnav Tripathy.

Wednesday, March 4, 2020

2:00 pm in 447 Altgeld Hall,Wednesday, March 4, 2020

#### Deformation and Obstruction for moduli of sheaves

###### Lutian Zhao (Illinois Math)

Abstract: In this talk, I’ll introduce the deformation theory for moduli of sheaves,. I’ll give a proof for the description of tangent space of moduli of sheaves and the condition for which this moduli space is smooth. The final goal of this talk is to introduce the construction for Simpson’s moduli space of sheaves.

Tuesday, March 10, 2020

3:00 pm in 243 Altgeld Hall,Tuesday, March 10, 2020

#### The critical filtration of Hurwitz spaces

###### George Shabat (Russian State University for the Humanities and Independent University of Moscow)

Abstract: Hurwitz spaces, introduced at the end of 19th century, consist of classes of isomorphism of pairs (algebraic curve, rational function on it), where a curve has a fixed genus and a function has a fixed degree. The strata of the filtration, to which the talk is devoted, are formed by the pairs, in which a function has a fixed number of \textit{critical values}. In every Hurwitz space the largest stratum (the \textit{Morse} one) is Zariski-open, while the lowest one consists of pairs in which the function has only three critical values, i.e. of \textit{Belyi pairs}. The considerable part of the talk will be devoted to the strata closest to the lowest ones, i.e. the so-called \textit{Fried families}. The combinatorial, algebro-geometric and arithmetic structures, related to these objects, will be considered, and some examples will be presented.