Department of

Mathematics


Seminar Calendar
for events the day of Thursday, December 9, 2004.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, December 9, 2004

1:00 pm in 241 Altgeld Hall,Thursday, December 9, 2004

Mystery Tales from India

Bruce Berndt (UIUC)

Abstract: We survey several results of Ramanujan whose origins are enigmatic, mysterious, and flabbergasting.

1:00 pm in Altgeld Hall 347,Thursday, December 9, 2004

Orderability of Artin monoids

Patrick Bahls (UIUC)

Abstract: The concept of orderability (of groups and monoids) is closely related to various other issues regarding these objects, such as local indicability and the Zero Divisor Conjecture. Not a great deal is known concerning orderability of Artin groups or their positive monoids. (For instance, right-angled Artin groups are bi-orderable, while braid groups are known to be left-orderable but not bi-orderable.) In this talk we will prove that the positive monoid of a large-type Artin group is left-orderable by generalizing a construction due to a student of P. Dehornoy.

2:00 pm in 343 Altgeld Hall,Thursday, December 9, 2004

Discrete-Time Models for an Individualís Life Insurance, Consumption, and Investment Decisions

Judy Zhu (UIUC Actuarial Science)

Abstract: An individual makes her/his life insurance and stock purchase decisions independently or jointly, depending on risk attitudes and the form of utility function. With an exponential utility function, life insurance and stock purchases are independent of each other. With a power utility function, life insurance and stock purchases are positively related with each other. Future income, bequest motive, risk attitude, and insurance premiums are the most significant factors affecting life insurance decisions. Risk attitudes, stock returns and volatilities are the most significant factors affecting stock purchase decisions. An individual will terminate a life insurance policy when future income is reduced, the bequest motive decreases, or the insurance premium or insurance surrender value increases. The findings from the one-period and two-period models are consistent: the individual purchases life insurance when s/he has a large future income, strong bequest motive, is more risk averse, and offered a cheaper insurance premium. S/he terminates a policy when those conditions no longer exist.

2:00 pm in Altgeld Hall 243,Thursday, December 9, 2004

SLE in multiply connected domains: Diffusions on moduli space and

Robert Bauer (UIUC)

Abstract: We discuss the extension of radial SLE to multiply connected planar domains. First, we extend Loewner's theory of slit mappings to multiply connected domains by establishing the radial Komatu-Loewner equation, and show that a simple curve from the boundary to the bulk is encoded by a motion on moduli space and a motion on the boundary of the domain. Then, we show that the vector-field describing the motion of the moduli is Lipschitz. We explain why this implies that "consistent", conformally invariant random simple curves are described by multidimensional diffusions, where one component is a motion on the boundary, and the other component is a motion on moduli space. We argue what the exact form of this diffusion is (up to a single real parameter k) in order to model boundaries of percolation clusters. Finally, we show that this moduli diffusion leads to random non-self-crossing curves satisfying the locality property if and only if k=6.

2:00 pm in 241 Altgeld Hall,Thursday, December 9, 2004

Differential arc spaces and regular types (continuation).

Anand Pillay (UIUC)

Abstract: Continuation of the talk given in the logic seminar on tuesday. Anand will hopefully give a proof of the theorem.

2:00 pm in Everett 168,Thursday, December 9, 2004

Henn's paper on Cohomology of Profinite groups, II

Nora Ganter (UIUC)

3:00 pm in 243 Altgeld Hall,Thursday, December 9, 2004

Peskine and Szpiro's proof of the Intersection Theorem, cont.

Bart Snapp   [email] (UIUC Math)

Abstract: In this talk I will present Peskine and Szpiro's proof of the Intersection Theorem. Specifically, I will show how to reduce the characteristic zero case to the characteristic p case. An attempt will be made to make this talk accessible to anyone who has taken a course in Commutative Algebra.

3:00 pm in 241 Altgeld Hall,Thursday, December 9, 2004

Differential arc spaces and regular types (continuation).

Anand Pillay (UIUC)

Abstract: Continuation of the talk given in the logic seminar on tuesday. Anand will hopefully give a proof of the theorem.

3:00 pm in 345 Altgeld Hall,Thursday, December 9, 2004

Spectral properties of a polyharmonic operator with limit-periodic potential

Young-Ran Lee (UIUC Math)

Abstract: We consider a polyharmonic operator: $$ H=(-\Delta)^l+\sum_{n=1}^{\infty} V_n(x),$$ where $V_n(x)$ is periodic with the periods growing exponentially as $2^n$ and the $L_{infty}$-norm decaying super-exponentially. We have shown that when $l>6$, a generalized version of the Bethe-Sommerfeld conjecture holds for this operator, in other words, its spectrum contains a semi-axis. We have proved also that there are eigenfunctions which are close to plane waves. (joint work with Yulia Karpeshina)

4:00 pm in Altgeld Hall 245,Thursday, December 9, 2004

Amenability, self-similarity and entropy

Vadim Kaimanovich (CNRS Rennes)

Abstract: We shall discuss a new development at the crossroads of Analysis, Algebra and Probability. Amenability (its definition going back to von Neumann) is, from the analytical point of view, the most natural generalization of finiteness or compactness. Namely, amenable groups are those which admit an invariant mean (rather than an invariant probability measure, which is the case for finite or compact groups). Groups acting by automorphisms of a homogeneous rooted tree (self-similar and automata groups, iterated monodromy groups) has recently become the object of an extensive study in the group theory, since even in the simplest situations such groups may have rather unusual properties. We shall describe a new technique for proving amenability of self-similar groups ("Munchhausen trick") developed by the author and based on using the notion of the asymptotic enropy of a random walk. This technique has recently lead to a proof of amenability for a large class of self-similar groups by Bartholdi, Nekrashevych, Virag and the author.

4:30 pm in 321 Altgeld Hall (lounge),Thursday, December 9, 2004

End-of-Semester Pizza Party

Abstract: We will have a pizza party in lieu of the grad student algebraic geometry seminar this week. Please come even if you haven't made it to seminar in a while --- we will also be planning for next semester.