Geometry Seminar
Date：11/15/2012 Thu.～11/16/2012 Fri.
Place:Tohoku Uviv.Aobayama Campus (Graduate School of Science)
http://www.math.tohoku.ac.jp/english/campus-e.html
-------------------
15th November (Thu)
-------------------
10:30 -- 12:00 Geomtry Seminar
Place：合同棟1201 (Physics and Natural Science Building)
Speaker：Benoit Collins
Title：random matrices, free probability and quantum information
15:00 -- 17:30 Geomtry Seminar
Place：合同棟801 (Physics and Natural Science Building)
Speaker：Paul Frank Baum
Title,1：BEYOND ELLIPTICITY
(Seminar talk about K-homology and index theory for non-elliptic operators)
Title,2：EXACT CROSSED-PRODUCTS : COUNTER-EXAMPLE REVISITED
(Seminar talk about corrected version of the BC (Baum-Connes) conjecture)
19:00 -- Party
-------------------
16th November (Fri)
-------------------
13:30 -- 14:30 Colloquium
Place：Kawai Hall
Speaker：Paul Frank Baum
Title：WHAT IS K-THEORY AND WHAT IS IT GOOD FOR?
--------------------------------
Organizers：
Motoko Kotani（Tohoku Univ.）
Tomohiro Fukaya（Tohoku Univ.）tomo(at)math.tohoku.ac.jp
--------------------------------
Abstract:
----
Benoit Collins
random matrices, free probability and quantum information
Random techniques are quite useful in classical information theory. In the same vein, it has been discovered in the last few years that random matrix theory can play a crucial role in the understanding of the behavior of random quantum channels. I will review a few very important problems in quantum information theory, and outline the random matrix techniques that have lead to a solution to some of these problems. In turn, quantum information becomes a source of interesting new random matrix models with unexpected properties. I will also explain the relation with free probability theory.
----
Paul Frank Baum
1. Seminar talk about K-homology and index theory for non-elliptic operators
BEYOND ELLIPTICITY
K-homology is the dual theory to K-theory. The BD (Baum-Douglas) isomorphism of Kasparov K-homology and K-cycle K-homology can be taken as providing a framework within which the Atiyah-Singer index theorem can be extended to certain non-elliptic operators. This talk will consider a class of non-elliptic differential operators on compact contact manifolds. These operators have been studied by a number of mathematicians. Working within the BD framework, the index problem will be solved for these operators. This is joint work with Erik van Erp.
2. Seminar talk about corrected version of the BC (Baum-Connes) conjecture
EXACT CROSSED-PRODUCTS : COUNTER-EXAMPLE REVISITED
A discrete group G which "contains" an expander in its Cayley graph is a counter-example to the Baum-Connes (BC) conjecture with coefficients. Some care must be taken with the definition of "contains". Using a method of E. Kirchberg, BC can be corrected. The correction is on the right side of BC. The left side remains unchanged. For exact groups (i.e. all groups except the Gromov group) both sides of BC remain unchanged. We can expect that in the corrected version of the conjecture, the expander counter-example (i.e. the Gromov group)is no longer a counter-example.
3. Colloquium talk on K-theory for a general mathematical audience
The talk will consist of four points.
#1. The basic definition of K-theory
#2. A brief history of K-theory
#3. Algebraic versus topological K-theory
#4. The unity of K-theory
This is a colloquium talk intended for non-specialists.
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