Seminar Calendar
for Algebraic Geometry events the next 12 months of Sunday, January 1, 2017.

.
events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    December 2016           January 2017          February 2017
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3    1  2  3  4  5  6  7             1  2  3  4
4  5  6  7  8  9 10    8  9 10 11 12 13 14    5  6  7  8  9 10 11
11 12 13 14 15 16 17   15 16 17 18 19 20 21   12 13 14 15 16 17 18
18 19 20 21 22 23 24   22 23 24 25 26 27 28   19 20 21 22 23 24 25
25 26 27 28 29 30 31   29 30 31               26 27 28



Thursday, January 19, 2017

3:00 pm   in 345 Altgeld Hall,  Thursday, January 19, 2017
 Del Edit Copy
Submitted by jjwen2.
 Organizational meeting

Tuesday, January 24, 2017

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, January 24, 2017
 Del Edit Copy
Submitted by katz.
 Yungfeng Jiang (U Kansas Math)On the Behrend function and its motivic version in Donaldson-Thomas theoryAbstract: The Behrend function, introduced by K. Behrend, is a fundamental tool in the study of Donaldson-Thomas invariants. In his foundational paper K. Behrend proves that the weighted Euler characteristic of the Donaldson-Thomas moduli space weighted by the Behrend function is the Donaldson-Thomas invariants defined by R. Thomas using virtual fundamental cycles. This makes the Donaldson-Thomas invariants motivic. In this talk I will talk about the basic notion of the Behrend function and apply it to several other interesting geometries. If time permits, I will also talk about the motivic version of the Behrend function and the famous Joyce-Song formula of the Behrend function identities.

Friday, January 27, 2017

3:00 pm   in 243 Altgeld Hall,  Friday, January 27, 2017
 Del Edit Copy
Submitted by jjwen2.
 Josh Wen (UIUC Math)Raindrop. Droptop. Symmetric functions from DAHA.Abstract: In symmetric function theory, various distinguished bases for the ring of (deformed) symmetric functions come from specifying an inner product on said ring and then performing Gram-Schmidt on the monomial symmetric functions. In the case of Jack polynomials, there is an alternative characterization as eigenfunctions for the Calogero-Sutherland operator. This operator gives a completely integrable system, hinting at some additional algebraic structure, and an investigation of this structure digs up the affine Hecke algebra. Work of Cherednik and Matsuo formalize this in terms of an isomorphism between the affine Knizhnik-Zamolodichikov (KZ) equation and the quantum many body problem. Looking at q-analogues yields a connection between the affine Hecke algebra and Macdonald polynomials by relating the quantum affine KZ equation and the Macdonald eigenvalue problem. All of this can be streamlined by circumventing the KZ equations via Cherednik's double affine Hecke algebra (DAHA). I hope to introduce various characters in this story and give a sense of why having a collection of commuting operators can be a great thing.

Tuesday, January 31, 2017

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, January 31, 2017
 Del Edit Copy
Submitted by rtramel.
 Tom Nevins (UIUC)Kirwan surjectivity for quiver varietiesAbstract: Many interesting hyperkahler, or more generally holomorphic symplectic, manifolds are constructed via hyperkahler/holomorphic symplectic reduction. For such a manifold there is a “hyperkahler Kirwan map,” from the equivariant cohomology of the original manifold to the reduced space. It is a long-standing question when this map is surjective (in the Kahler rather than hyperkahler case, this has been known for decades thanks to work of Atiyah-Bott and Kirwan). I’ll describe a resolution of the question (joint work with K. McGerty) for Nakajima quiver varieties: their cohomology is generated by Chern classes of “tautological bundles.” If there is time, I will explain that this is a particular instance of a general story in noncommutative geometry. The talk will not assume prior familiarity with any of the notions above.

Friday, February 3, 2017

3:00 pm   in 243 Altgeld Hall,  Friday, February 3, 2017
 Del Edit Copy
Submitted by jjwen2.
 Eliana Duarte (UIUC Math)Syzygies and Implicitization of tensor product surfacesAbstract: A tensor product surface is the closure of the image of a map $\lambda:\mathbb{P}^1\times \mathbb{P}^1\to \mathbb{P}^3$. These surfaces arise in geometric modeling and in this context it is useful to know the implicit equation of $\lambda$ in $\mathbb{P}^{3}$. Currently, syzygies and Rees algebras provide the fastest and most versatile method to find implicit equations of parameterized surfaces. Knowing the structure of the syzygies of the polynomials that define the map $\lambda$ allows us to formulate faster algorithms for implicitization of these surfaces and also to understand their singularities. We show that for tensor product surfaces without basepoints, the existence of a linear syzygy imposes strong conditions on the structure of the syzygies that determine the implicit equation. For tensor product surfaces with basepoints we show that the syzygies that determine the implicit equation of $\lambda$ are closely related to the geometry of the set of points at which $\lambda$ is undefined.

Wednesday, February 8, 2017

Doob Colloquium
3:00 pm   in 243 Altgeld Hall,  Wednesday, February 8, 2017
 Del Edit Copy
Submitted by lescobar.
 Rebecca Tramel (UIUC)Stability and wall-crossing in algebraic geometryAbstract: I will discuss two notions of stability in algebraic geometry: slope stability of vector bundles on curves, and Bridgeland stability for complexes of sheaves on smooth varieties. I will try and motivate both of these definitions with questions from algebraic geometry and from physics. I will then work through a few detailed examples to show how varying our notion of stability affects the set of stable objects, and how this relates to the geometry of the space we are studying.

Friday, February 10, 2017

3:00 pm   in 243 Altgeld Hall,  Friday, February 10, 2017
 Del Edit Copy
Submitted by jjwen2.
 Matej Penciak (UIUC Math)The KP-CM correspondenceAbstract: In this talk I will describe how two seemingly unrelated integrable systems have an unexpected connection. I will begin with the classical story first worked out by Airault, McKean, and Moser. I will then describe a more modern interpretation of the relation due to Ben-Zvi and Nevins.

Friday, February 17, 2017

3:00 pm   in 243 Altgeld Hall,  Friday, February 17, 2017
 Del Edit Copy
Submitted by jjwen2.
 Lutian Zhao (UIUC Math)What is a Topological Quantum Field Theory?Abstract: In this talk we will introduce the physicists' definition of topological quantum field theory, mainly focusing on cohomological quantum field theory introduced by Witten. We will discuss topological twisting and see what topological invariant is actually computed. If time permits, we will see how Gromov-Witten invariants are constructed by physics.

Friday, February 24, 2017

3:00 pm   in 243 Altgeld Hall,  Friday, February 24, 2017
 Del Edit Copy
Submitted by jjwen2.
 Sungwoo Nam (UIUC Math)Quantum cohomology of Grassmannians and Gromov-Witten invariantsAbstract: As a deformation of classical cohomology ring, (small) quantum cohomology ring of Grassmannians has a nice description in terms of quantum Schubert classes and it has (3 point, genus 0) Gromov-Witten invariants as its structure constants. In this talk, we will describe how 'quantum corrections' can be made to obtain quantum Schubert calculus from classical Schubert calculus. After studying its structure, we will see that the Gromov-Witten invariants, which define ring structure of quantum cohomology of Grassmannians, are equal to the classical intersection number of two-step flag varieties. If time permits, we will discuss classical and quantum Littlewood-Richardson rule using triangular puzzles.

Monday, February 27, 2017

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Monday, February 27, 2017
 Del Edit Copy
Submitted by laugesen.
 Hal Schenck (Department of Mathematics, University of Illinois)Algebra, Combinatorics, GeometryAbstract: I'll give an overview of the spectacular success of algebraic methods in studying problems in discrete geometry and combinatorics. First we'll discuss the face vector (number of vertices, edges, etc.) of a convex polytope and recall Euler's famous formula for polytopes of dimension 3. Then we'll discuss graded rings, focusing on polynomial rings and quotients. Associated to a simplicial polytope P (every face is "like" a triangle) is a graded ring called the Stanley-Reisner ring, which "remembers" everything about P, and gives a beautiful algebra/combinatorics dictionary. I will sketch Stanley's solution to a famous conjecture using this machinery, and also touch on connections between P and toric varieties, which are objects arising in algebraic geometry.

Tuesday, February 28, 2017

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, February 28, 2017
 Del Edit Copy
Submitted by rtramel.
 Sheldon Katz (UIUC)To Be Announced

Tuesday, March 7, 2017

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, March 7, 2017
 Del Edit Copy
Submitted by rtramel.
 Andras Lorincz (Purdue University)To Be Announced

Tuesday, March 14, 2017

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, March 14, 2017
 Del Edit Copy
Submitted by rtramel.
 Junwu Tu (University of Missouri )To Be Announced

Tuesday, March 28, 2017

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, March 28, 2017
 Del Edit Copy
Submitted by rtramel.
 John Lesieutre (UIC)To Be Announced

Tuesday, April 4, 2017

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, April 4, 2017
 Del Edit Copy
Submitted by rtramel.
 Tatsunari Watanabe (Purdue University)To Be Announced

Tuesday, April 11, 2017

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, April 11, 2017
 Del Edit Copy
Submitted by rtramel.
 Deepam Patel (Purdue University)To Be Announced

Tuesday, April 18, 2017

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, April 18, 2017
 Del Edit Copy
Submitted by katz.
 Rahul Pandharipande (ETH Zurich)Stable quotients and the B-modelAbstract: I will give an account of recent progress on stable quotient invariants, especially from the point of view of the B-model and present a geometrical derivation of the holomorphic anomaly equation for local CY cases (joint work with Hyenho Lho).