Lectures

 

Lecture: Density of the Ordinary Locus in the Hilbert-Siegel Moduli Spaces
 
TitleDensity of the Ordinary Locus in the Hilbert-Siegel Moduli Spaces
 
SpeakerJafu Yu  Academia Sinica, Taiwan
 
Date: 4:00-5:00 pm; February 28 (Thursday); 2013
 
PlaceConference Room A404, Department of Mathematical Sciences
 
ContactLinsheng Yin
 
 
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Lecture: On Tensor Powers of t-motives and the Multiple Zeta Values.
 
TitleOn Tensor Powers of t-motives and the Multiple Zeta Values.
 
SpeakerJing Yu, National Taiwan University
 
Date:3:30-5:00 pm; April 2, April 9, 2013  
10:00-11:30 am; April 4, April 11; 2013
 
PlaceConference Room A404, Department of Mathematical Sciences
 
The four lectures entitled respectively
 
1. Tensor Powers of the Carlitz module, and the special Carlitz zeta values.

2. t-modules ad t-motives. Papanikolas theory.

3. The multiple zeta values of Thakur, and t-motives

4. Linear independence for monomials of multiple zeta values.

Abstract: I shall first recall the Anderson-Thakur theory on tensor powers, and motivic interpretation of the multiple zeta values. The determination of all algebraic relations among Carlitz zeta values by Chang-Yu, the analogue of Baker's linear independence for polylogarithms, and the recent progress on a strong form of Goncharov's conjecture in positive characteristic, and the the problem of being Eulerian for multiple zeta values.
ContactLinsheng Yin
 
 
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Lecture: Tightening a Copositive Relaxation for Standard Quadratic Optimization Problems
 
TitleTightening a Copositive Relaxation for Standard Quadratic Optimization Problems
 
SpeakerProf. Ruilin Xu, National Cheng Kung University, Taiwan
 
Time4:00-5:00 pm; April 1; 2013
 
PlaceConference Room A404, Department of Mathematical Sciences
 
Abstract: In this talk, we focus on the problem of improving the semidefinite programming (SDP) relaxations for the standard quadratic optimization problem (standard QP in short) that concerns with minimizing a quadratic form over a simplex. We first analyze the duality gap between the standard QP and one of its SDP relaxations known as “strengthened Shor's relaxation”. To estimate the duality gap, we utilize the duality information of the SDP relaxation to construct a graph G. The estimation can be then reduced to a two-phase problem of enumerating first all the minimal vertex covers of G and solving next a family of second-order cone programming problems. When there is a nonzero duality gap, this duality gap estimation can lead to a strictly tighter lower bound than the strengthened Shor's SDP bound. With the duality gap estimation improving scheme, we develop further a heuristic algorithm for obtaining a good approximate solution for standard QP.
 
ContactWenxun Xing
 
 
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Lecture: How Negative Can a Negative Ion Be?
 
TitleHow Negative Can a Negative Ion Be?
SpeakerHeinz Siedentop, Ludwig Maximilian Muenchen Unitversitaet
Date: 3:30-4:30 pm; March14; 2013
 
PlaceConference Room A304, Department of Mathematical Sciences
Abstract: We give an overview over some conjectured and known facts about the maximal number of electrons that atoms and quantum dots can bind. We discuss this in various contexts: experimentally, in simple density functionals, for atoms described by Schroedinger operators, and eventually for artificial atoms, so called quantum dots, in a graphene layer described by a pseudo-relativistic operator. The main result is based on joined work with Michael Handrek (Munich) and on a general Hardy type inequality obtained with Li Chen (Peking).
ContactLi Chen