Department of

Mathematics


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

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More information on this calendar program is available.
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
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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

3:00 pm in 243 Altgeld Hall,Tuesday, February 4, 2020

Moduli spaces of Lagrangians in symplectic topology and mirror symmetry

James Pascaleff (UIUC)

Abstract: Moduli spaces of Lagrangians (as objects in Fukaya categories), and the geometry on such moduli spaces, may be used to understand problems in symplectic topology and mirror symmetry. In this talk, I will introduce these ideas and give an example showing how to use symplectic topology to solve a problem about Laurent polynomials (based on joint work with Dmitry Tonkonog).

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, Iíll introduce the deformation theory for moduli of sheaves,. Iíll 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 Simpsonís moduli space of sheaves.

Thursday, March 5, 2020

3:00 pm in 347 Altgeld Hall,Thursday, March 5, 2020

Fulton's Conjecture, Extremal Rays, and Applications to Saturation

Joshua Kiers   [email] (University of North Carolina, Chapel Hill)

Abstract: We begin by recalling a conjecture of Fulton on Littlewood-Richardson coefficients and discussing two generalizations. With a little lemma from algebraic geometry, we find ourselves on the way to naming the extremal rays of the "eigencone'' of asymptotic solutions to the branching question in representation theory of semisimple Lie groups. After giving an algorithm for finding all such extremal rays, generalizing some prior work joint with P. Belkale, we report on progress on the saturation conjecture for types $D_5$, $D_6$, and $E_6$.

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.