Constructing Higher Order Elements in Finite Fields

Speaker: 

Qi Cheng

Speaker Link: 

http://www.cs.ou.edu/~qcheng/

Institution: 

University of Oklahoma

Time: 

Wednesday, March 21, 2012 - 10:00am to 11:00am

Host: 

Daqing Wan

Location: 

440R

Every finite field has many multiplicative generators. However,
finding one in polynomial time is an important open problem .
In fact, even finding elements of high order has not been solved
satisfactorily. In this paper, we present an algorithm that for any
positive integer $c$ and prime power $q$, finding an element of
order $\exp(\Omega(\sqrt{q^c}) ) $ in the finite field $\F_{q^{(q^c-1)/(q-1)}}$
in deterministic time $(q^c)^{O(1)}$. We also show that there are
$\exp(\Omega(\sqrt{q^c}) ) $ many weak keys for the discrete logarithm problems
in those fields with respect to certain bases.

On Bruin-Troubetzkoy family

Speaker: 

Scott Northrup

Institution: 

UCI

Time: 

Friday, March 16, 2012 - 2:00pm to 3:00pm

Location: 

RH 440R

Bruin-Troubetzkoy family is a two parameter family of interval translation mappings. It was studied using a renormalization procedure that provides a satisfactory description of its dynamical properties. In the talk we will describe this procedure, list the known properties of the family, and state some new results.

Truth Values comes to UCI, Thursday, April 26 at the Irvine Barclay Theatre

As part of its ten year anniversary, UCI ADVANCE will host a west coast performance of "Truth Values: One Girl’s Romp through M.I.T.’s Male Math Maze" at 7:00 PM on Thursday, April 26, 2012 at the Irvine Barclay Theatre. In this compelling one-woman show, which has earned raves from critics and stirred audiences to standing ovations, Gioia de Cari dramatizes the experience of a female graduate student in the Mathematics Department at M.I.T. as she negotiates the politics of power and gender in the academy.

Inverse problems and free-discontinuity problems

Speaker: 

Luca Rondi

Institution: 

University of Trieste

Time: 

Tuesday, March 13, 2012 - 2:00pm to 3:00pm

Location: 

RH306

Many techniques developed for free-discontinuity problems, arising for example in imaging or in fracture mechanics, may be successfully applied to reconstruction methods for inverse problems whose unknowns may be characterized by discontinuous functions.

We show the validity of this approach both from the theoretical point of view, by a convergence analysis, and from the numerical point of view.

The structure of ideals II

Speaker: 

Monroe Eskew

Institution: 

UCI

Time: 

Monday, March 12, 2012 - 4:00pm to 5:30pm

Host: 

Martin Zeman

Location: 

RH 440R

We present a proof of a theorem of Gitik and Shelah that places limits on the structure of quotient algebras by sigma-additive ideals. We will start by showing connections between Cohen forcing and Baire category on the reals. Then by using generic ultrapowers, we will prove that no sigma-additive ideal yields an atomless algebra with a countable dense subset. We will discuss connections with Ulam's measure problem: How many measures does it take to measure all sets of reals?

Local estimates in 3-dimensional Ricci flow

Speaker: 

Guoyi Xu

Institution: 

UC Irvine

Time: 

Tuesday, April 24, 2012 - 4:00pm

Location: 

RH 306

We study curvature estimates of Ricci flow on complete 3-dim manifolds
without bounded curvature assumptions. Especially, from a more general
curvature preservation condition, we derived that nonnegative Ricci
curvature is preserved for any complete solution of 3-dim Ricci flow. A local
version of Hamilton-Ivey estimates is also obtained. Using that the nonnegative
Ricci is preserved under any 3-dim Ricci flow complete solution, we can prove the strong uniqueness of the Ricci flow with bounded nonnegative Ricci curvature and uniform injective radius lower bound as initial assumptions. This is joint work with Bing-Long Chen and Zhuhong Zhang.

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