Department of

Mathematics


Seminar Calendar
for events the day of Thursday, February 2, 2006.

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Thursday, February 2, 2006

1:00 pm in 347 Altgeld Hall,Thursday, February 2, 2006

Uniform convergence groups and the mapping class group.

Chris Leininger (UIUC Math)

Abstract: Abstract: I'll discuss both positive an negative results relating the notion of uniform convergence group to that of convex cocompactness in the mapping class group. This is joint work with Richard Kent.

1:00 pm in 241 Altgeld Hall,Thursday, February 2, 2006

Weighted Trigonometric Sums Over a Half-Period

O -Yeat Chan (UIUC)

Abstract: Let $f(z)$ be a quotient of trigonometric functions. Suppose $f(z)$ has period $k$, an odd integer. We use a contour integral to evaluate the sum $$\sum a_i f(i)$$ for any sequence of complex numbers $a_i$ in terms of the Fourier coefficients of $f$. This work generalizes a paper by Berndt and Zaharescu that considered sums weighted by real, odd, non-principal Dirichlet characters.

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

Some category theory (cont'd)

Shivi Bansal   [email] (UIUC Math)

Abstract: We will finish describing triangulated categories, their truncations and cores. To wrap up, we will see an important example of a core of a triangulated category.

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

Iwasawa Theory

Tim Kilbourn (UIUC Math)

Abstract: (RAP Elliptic Curves and Iwasawa Theory, Part 2) This week is the second and last part of a review of results from Iwasawa Theory.

3:00 pm in 345 Altgeld Hall,Thursday, February 2, 2006

Generalized 3G theorem, non-local Schrodinger operator and relativistic stable process on non-smooth open sets

Panki Kim   [email] (UIUC Math)

Abstract: When G is Green function on a domain, we say that the 3G theorem is true if G(x,z)G(z,w)/G(x,w) is less than c g(|x-z|) g(|z-w|) /g(|x-w|) where g(|x-y|) is Green function in R^d. 3G theorem above is closely related to Kato class, the conditional Gauge theorem and local Schrodinger operators. In this talk, we will discuss about the generalized 3G theorem; The generalized 3G form is G(x,y)G(z,w)/G(x,w) where y may be different from z. This 3G form appears in non-local Schrodinger operator theory. The generalized 3G theorem is equally important in non-local Schrodinger operators as is the classical 3G theorem in local Schrodinger operators. Using the generalized 3G theorem, we give a concrete form of non-local Kato class. We will also discuss other consequences of the generalized 3G theorem. In particular, some boundary potential theory of relativistic stable process in non-smooth open sets. This is a joint work with Young-Ran Lee.