UIUC Dept. of Mathematics Seminar Calendar

      July 2008             August 2008           September 2008   
 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                   1  2       1  2  3  4  5  6
  6  7  8  9 10 11 12    3  4  5  6  7  8  9    7  8  9 10 11 12 13
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 20 21 22 23 24 25 26   17 18 19 20 21 22 23   21 22 23 24 25 26 27
 27 28 29 30 31         24 25 26 27 28 29 30   28 29 30            
                        31

Wednesday, September 3, 2008

Graduate Student Algebraic Geometry Seminar
4:00 pm in 143 Altgeld Hall, Wednesday, September 3, 2008

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Submitted by sheshman.

Artan Sheshmani [email] (Department of Mathematics, University of Illinois)
(Topic changed!): Stable ADHM sheaves and their moduli spaces
Abstract: I will talk about ADHM sheaves ,stable ADHM sheaves and their moduli spaces, If I have time I will also talk about relation between ADHM sheaves and relative Beilinson spectral sequence, This talk may be technical to some extent, familiarity with Grothendieck's hyper-cohomology and Basic moduli theory would be very helpful.

Thursday, September 4, 2008

Tuesday, September 9, 2008

Algebraic Geometry Seminar
3:00 pm in 243 Altgeld Hall, Tuesday, September 9, 2008

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Submitted by nevins.

David Smyth (Harvard)
Compact moduli of singular curves: A case study in genus one
Abstract: We define an infinite sequence of isolated curve singularities, the elliptic $m$-fold points, and an associated sequence of stability conditions for $n$-pointed curves of genus one, which generalizes the usual notion of Deligne-Mumford stability. The maps between the corresponding moduli spaces can be interpreted as divisorial contractions and flips (in the sense of Mori theory). We will explain how this phenomena gives insight into the general problem (initiated by B. Hassett) of understanding the canonical model of moduli space of stable curves of genus g for g>>0.

Wednesday, September 10, 2008

Wednesday, September 17, 2008

Friday, September 19, 2008

Tuesday, September 23, 2008

Wednesday, September 24, 2008

Tuesday, September 30, 2008

Wednesday, October 1, 2008

Tuesday, October 7, 2008

Wednesday, October 8, 2008

Thursday, October 9, 2008

Tuesday, October 14, 2008

Algebraic Geometry Seminar
3:00 pm in 243 Altgeld Hall, Tuesday, October 14, 2008

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Submitted by nevins.

Zach Teitler (Texas A & M)
Bounding Hilbert functions of fat point schemes
Abstract: Let A be a fat point scheme in the plane. Typically one knows a set of curves that pass through some of the points of support of A. For example, one might know which sets of points in the support of A are collinear. I will demonstrate how to use this information to give upper and lower bounds for the Hilbert function of A. This leads to surprisingly good bounds and even a simple criterion for when the bounds coincide, so in many cases we get an exact computation of the Hilbert function of A. The technical idea is an inductive reduction: We reduce A along one of the lines passing through points of A, and relate the Hilbert function of A with the Hilbert function of the reduced scheme. In low degrees, this inductive step is simply Bezout�s theorem. The extension to arbitrary degrees is still elementary, and well-illustrated by examples. (This is joint work with Susan Cooper and Brian Harbourne.)

Wednesday, October 15, 2008

Tuesday, October 21, 2008

Algebraic Geometry Seminar
3:00 pm in 243 Altgeld Hall, Tuesday, October 21, 2008

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Submitted by nevins.

Prakash Belkale (University of North Carolina)
The monodromy of the Hitchin/WZW connection, and applications to strange dualities
Abstract: Non abelian theta functions, which generalise the classical theta functions on the Jacobian of a curve X, are associated to a group G, an algebraic curve X and a level k. As the curve X moves in its moduli space, the spaces of non abelian theta functions carry a connection. It is an open problem to determine the monodromy of this projective connection and to prove the physics expectation that it is unitary. I will review some of these questions. If G->H is a map of groups, H-theta functions map to G-theta functions. I will discuss the problem of determining when these maps are flat, with applications to ``strange dualities''.

Wednesday, October 22, 2008

Tuesday, October 28, 2008

Algebraic Geometry Seminar
3:00 pm in 243 Altgeld Hall, Tuesday, October 28, 2008

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Submitted by nevins.

Karl Schwede (University of Michigan)
F-singularities and relations with the singularities of birational geometry
Abstract: For the past 30 years, people have studied relations between singularities defined by the action of Frobenius in positive characteristic and singularities defined by a resolution in characteristic zero. I will sketch how some of these relations work, and describe recent work of mine on a positive characteristic p analogue of log canonical-centers (which it turns out have themselves been studied before). I will explain the very natural way in which Q-divisors \Delta such that K_X + \Delta is Q-Cartier appear in the positive characteristic setting. Finally, I will also explain recent work on local versions of F-(inversion of) (sub)adjunction on F-purity in positive characteristic.

Wednesday, October 29, 2008

Math 499: Introduction to Graduate Mathematics
4:00 pm in 245 Altgeld Hall, Wednesday, October 29, 2008

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Submitted by seminar.

Alex Yong (Department of Mathematics, University of Illinois)
Algebraic Combinatorics
Abstract: Algebraic combinatorics is concerned with interactions between combinatorics and other areas of mathematics, such as:

algebraic geometry
representation theory
commutative algebra
algebraic topology

One central theme in the subject is to give proofs of the non-negativity of integers, by obtaining combinatorial rules for them.

I'll give two core examples. The first is about the "Littlewood-Richardson numbers", which arise, e.g., in the intersection theory of Grassmannians, the representation theory of GL_n, and in eigenvalue problems about Hermitian matrices. The second discusses "totally positive matrices" (square matrices whose sub-determinants are all positive), a topic connected to: oscillations in mechanical systems, stochastic processes and approximation theory, and planar resistor networks.

Thursday, October 30, 2008

Differential Geometry Seminar
3:00 pm in 347 Altgeld Hall, Thursday, October 30, 2008

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Submitted by clein.

Graeme Wilkin (Johns Hopkins)
Moment map flows and algebraic geometry.
Abstract: A common theme in symplectic geometry is an expected relationship between a symplectic quotient and a geometric invariant theory quotient. This is known as the "Hitchin-Kobayashi correspondence", and has been proven for many cases of interest using geometric flow techniques, for example the Donaldson-Uhlenbeck-Yau theorem for holomorphic bundles over compact Kahler manifolds. Work of Daskalopoulos and Wentworth for the Yang-Mills flow over Kahler surfaces describes the limit of the flow in terms of an algebraic object: the Harder-Narasimhan-Seshadri filtration of a holomorphic bundle. This can be viewed as an "unstable Hitchin-Kobayashi correspondence". In this talk I will describe how this theorem can be extended to moment map flows on the space of Higgs bundles over a compact Riemann surface, and also on the space of representations of a quiver. The work on representations of a quiver is joint with Megumi Harada of McMaster University.

Tuesday, November 4, 2008

Tuesday, November 11, 2008

Graph Theory and Combinatorics
3:00 pm in 241 Altgeld Hall, Tuesday, November 11, 2008

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Submitted by west.

Alexander Yong (UIUC Math)
Positivity in Algebraic Combinatorics
Abstract: Algebraic combinatorics is concerned with interactions between combinatorics and other areas of mathematics, such as:
* algebraic geometry
* representation theory
* commutative algebra
* algebraic topology
One central theme in the subject is to give proofs of the non-negativity of integers by obtaining combinatorial rules for them. I'll give two core examples. The first is about the "Littlewood-Richardson numbers", which arise, e.g., in the intersection theory of Grassmannians, the representation theory of GL_n, and in eigenvalue problems about Hermitian matrices. The second discusses "totally positive matrices" (square matrices whose sub-determinants are all positive), a topic connected to oscillations in mechanical systems, stochastic processes and approximation theory, and planar resistor networks.

Wednesday, November 12, 2008

Graduate Student Algebraic Geometry Seminar
4:00 pm in 143 Altgeld Hall, Wednesday, November 12, 2008

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Submitted by choi29.

Li Li [email] (UIUC Math)
Decomposition Theorem and Algebraic geometry
Abstract: These talks give an introduction to the intersection cohomology, perverse sheaf and the Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber. I will first focus on two concrete examples: the resolution of surface singularities and the map from a surface to a curve. Then we will talk on perverse sheaves and the general form of the Decomposition Theorem. Finally we talk about some applications of the Decomposition Theorem, one of which is to compute the Poincare polynomials of Hilbert schemes.

Tuesday, November 18, 2008

Friday, December 5, 2008

Tuesday, December 9, 2008

Tuesday, January 27, 2009

Wednesday, February 4, 2009

Tuesday, February 17, 2009

Thursday, February 19, 2009

Mathematics Colloquium
4:00 pm in 245 Altgeld Hall, Thursday, February 19, 2009

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Submitted by nmd.

Allen Knutson (Cornell University)
Why do matrices commute? Algebraic geometry meets statistical mechanics
Abstract: The matrix equations M^2 = 0 are quadratic, so to derive the linear equation Trace(M)=0 from them requires nonalgebraic operations. Are there corresponding "surprising" equations implied by the matrix equation XY=YX? This question was posed in the '60s, and still nobody knows. Even the (normalized) volume of this space &ob;(X,Y) : XY=YX&cb; is very difficult to compute for large matrices, and until recently was only known to start 1,3,31,1145.

I'll talk about a bunch of related spaces of matrices, some of which are provably harder and some easier to understand than the commuting scheme &ob;(X,Y) : XY=YX&cb;, and the volumes of these spaces. Then I'll explain how physicists came up with the same set of numbers from a statistical mechanical model (making them much easier to compute), and why they are indeed the same.

Some of this work is joint with Paul Zinn-Justin.

Tuesday, February 24, 2009

Tuesday, March 3, 2009

Tuesday, March 10, 2009

Algebraic Geometry Seminar
3:00 pm in 243 Altgeld Hall, Tuesday, March 10, 2009

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Submitted by nevins.

Susan Sierra (University of Washington)
Transversality and noncommutative geometry
Abstract: Let Z and Y be closed subvarieties of a variety X. We say that Z and Y are _homologically_transverse_ if the higher Tor's of their structure sheaves all vanish. Now let G be an algebraic group acting on X. We give conditions on Z that ensure that for any Y, the general translate of Z under the action of G is homologically transverse to Y. This result generalizes a recent result of Miller and Speyer for transitive group actions and ultimately goes back to the classical Kleiman-Bertini theorem. We give applications to noncommutative algebraic geometry, including the classification of noncommutative surfaces.

Tuesday, March 17, 2009

Algebraic Geometry Seminar
3:00 pm in 243 Altgeld Hall, Tuesday, March 17, 2009

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Submitted by nevins.

Donghoon Hyeon (Marshall University)
A new look at the moduli space of hyperelliptic curves
Abstract: There are two natural ways to compactify the moduli space of smooth hyperelliptic curves of genus g: one is to take the closure in the moduli space of stable curves of genus g, and the other is to construct the GIT quotient of semistable binary forms of degree 2g + 2. Avritzer and Lange showed that there is a projective birational morphism f from the former to the latter extending the natural isomorphism between the loci of smooth curves. By carrying out a log minimal model program, we prove that f decomposes into a series of divisorial contractions collapsing the boundary divisors in natural order. We also obtain a conjectural formula for critical values in the log MMP for the moduli of stable hyperelliptic curves which are also expected to be critical values for the log MMP for the moduli of stable curves. They are then identified with the values from a formula obtained by considering the GIT stability of curves. This suggests that log canonical models can be constructed as GIT quotients of Hilbert scheme of curves that are 'rationally' semistable.

Graph Theory and Combinatorics
3:00 pm in 241 Altgeld Hall, Tuesday, March 17, 2009

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Submitted by west.

Hal Schenck (UIUC Math)
Graphs, hyperplane arrangements, and algebra
Abstract: Associated to a simple graph G with vertex set V is a hyperplane arrangement A, which is a finite set of hyperplanes in the vector space K^|V| (typically K is the complex or real numbers). Each edge (i,j) of G gives rise to a hyperplane, defined by the vanishing of the linear form x_i-x_j. I'll spend the first half of the talk describing examples and the basic translation between graph-theoretic concepts and the analogous concepts in algebraic geometry. In the second part I'll describe two basic algebraic objects associated to arrangements, as well as several open conjectures about these objects.

Thursday, March 19, 2009

Tuesday, March 31, 2009

Tuesday, April 14, 2009

Wednesday, April 29, 2009

Graduate Student Topology and Geometry Seminar
1:00 pm in Altgeld Hall 147, Wednesday, April 29, 2009

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Submitted by reldred2.

Pat Szuta (UIUC Math)
Hochschild, Negative, Cyclic, and Periodic Homologies of Exact Categories
Abstract: K-theory is a powerful tool with applications in algebraic geometry, algebraic topology and number theory, with two main flavors, Algebraic and Topological. Analogous to how homology groups can be used to approximate homotopy groups, we use topological Hochschild Homology (and related equivariant constructions) to approximate Algebraic K-theory. In this talk, we'll discuss Hochschild, Negative, Cyclic, and Periodic homologies of exact categories (categories with exact sequences). Our primary focus will be on the relationship between these theories as invariants of rings.