Department of

Mathematics


Seminar Calendar
for events the day of Thursday, February 23, 2006.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, February 23, 2006

1:00 pm in Altgeld Hall 347,Thursday, February 23, 2006

Groups with free regular length functions in Z^n

Denis Serbin (McGill University)

Abstract: Finding description of finitely generated groups acting freely on Lambda-trees, or, equivalently groups having free length functions in Lambda (where Lambda is an ordered abelian group) is one of the major problems in Geometric Group Theory. This problem was solved for some special cases of Lambda but still is far from being solved in the general case. In my talk, at first, I'm going to introduce a natural restriction on length function which is called the regularity condition. Then I'm going to present the description of finitely generated groups with regular free length functions in Z^n, and to discuss why regularity condition is important. This is a joint work with O. Kharlampovich, A. Myasnikov and V. Remeslennikov.

2:00 pm in 243 Altgeld Hall,Thursday, February 23, 2006

Doubling conditions, monotonicity, and quasiconformal mappings

Leonid Kovalev (Texas A&M University)

Abstract: Indefinite integrals of doubling measures on the real line exhibit some (although not all) properties of quasiconformal mappings. Generalizing this observation, we construct quasiconformal mappings by a kind of "indefinite integration" of doubling measures on R^n. We also introduce a stronger version of the doubling condition that may (or may not) characterize the Jacobians of certain monotone and quasiconformal mappings. This is an ongoing joint work with Diego Maldonado.

2:00 pm in 241 Altgeld Hall,Thursday, February 23, 2006

Elliptic Curves II

Eric landquist (UIUC Math)

Abstract: (RAP Elliptic Curves and Iwasawa Theory, Part 4) This week completes a review of results on Elliptic Curves. We discuss the Weak Mordell-Weil Theorem, Selmer groups and Tate-Shavarevich groups.

2:00 pm in 443 Altgeld Hall,Thursday, February 23, 2006

Distributions, integrability and contact geometry

Christopher Lee (UIUC Math)

Abstract: I will begin by discussing some basics in the theory of distributions, starting with the definition and making some remarks on integral/involutive distributions, the Frobenius theorem, and curvature of distributions. Following this, we will examine special distributions: contact structures on manifolds.

3:00 pm in 345 Altgeld Hall,Thursday, February 23, 2006

Missing the hole: Conformally invariant random curves in ring domains and elliptic functions

Robert Bauer (UIUC Math)

Abstract: There is only one measure on simple curves which is conformally invariant, domain Markovian, and a restriction measure---the conjectured scaling limit of the self-avoiding random walk. I will eplain why there is only one and then study this measure in ring domains. Here, elliptic functions play a prominent role, and their interplay with the Markovian property leads to a partial differential equation with doubly periodic coefficients. Throughout, I will emphasize concepts so that the talk should be accessible to a general audience.

3:00 pm in 243 Altgeld Hall,Thursday, February 23, 2006

On The Upper Semi-Continuity of Hilbert-Kunz Multiplicity

Jinjia Li   [email] (UIUC Math)

Abstract: I will discuss a recent paper by Enescu and Shimomoto on the upper semi-continuity of the Hilbert-Kunz multiplicity. I will begin with a introduction/overview of the Hilbert-Kunz multiplicity. This talk only assumes minimum background in commutative algebra (e.g. MATH 502).

3:00 pm in 243 Altgeld Hall,Thursday, February 23, 2006

On The Upper Semi-Continuity of Hilbert-Kunz Multiplicity

Jinjia Li   [email] (UIUC Math)

Abstract: I will discuss a recent paper by Enescu and Shimomoto on the upper semi-continuity of the Hilbert-Kunz multiplicity. I will begin with a introduction/overview of the Hilbert-Kunz multiplicity. This talk only assumes minimum background in commutative algebra (e.g. MATH 502).

7:00 pm in 245 Altgeld Hall,Thursday, February 23, 2006

Math video - Outside In

Abstract: Come join the math club MATRIX as we watch a short (22-minute) film about turning spheres inside out.