January 16, 2017 - January 20, 2017
Public Access Category: All |
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- Time:
- 3:30pm-5:00pm
- Location:
- Room 114
- Description:
- Title: Jannsen's theorem on semi-simplicity - 1
Abstract: In these lectures we shall introduce motives and present results
in Jannsen's paper, which say that the "conjectural" category of motives
is semisimple abelian iff the adequate equivalence relation taken is
numerical equivalence. We shall also explain what is still "conjectural"
about this.
- Time:
- 4:00pm-5:00pm
- Location:
- Ramanujan Hall
- Description:
- Speaker: Prof. Hrushikesh N. Mhaskar, California Institute of Technology, Pasadena, and Claremont Graduate University, Claremont.
Title: Introduction to machine learning and approximation theory
Abstract: We will point out the relevance of approximation theory to
machine learning problems and review classical concepts of
approximation theory using trigonometric polynomial approximation of
periodic functions as a case study.
- Time:
- 3:30pm-5:00pm
- Location:
- Room 216, Maths Building
- Description:
- Title: Diophantine approximation on the plane by SL(2,$\mathbb Z$) orbits.
Abstract: It is known that under the action of SL(2,$\mathbb Z$) on the plane the orbit of any vector which is not a multiple of a rational vector, is dense in the plane. Thus any vector in the plane can be approximated by points on such an orbit. This talk will discuss certain quantitative aspects of such an approximation.
- Time:
- 4:00pm-5:00pm
- Location:
- Ramanujan Hall
- Description:
- Speaker: Anne-Marie Aubert, Institut de Mathematiques de Jussieu, France
Title: Preservation and non-preservation of depth under the local Langlands correspondence.
Abstract:
A central role in the representation theory of reductive p-adic groups is played by the local Langlands correspondence. It is known to exist in particular for the inner forms of general and special linear groups,
and to preserve interesting arithmetic information, like local L-functions and epsilon?-factors. Another
invariant that makes sense on both sides of the correspondence is depth. This notion will be introduced in the talk, and we will describe the known results regarding its transformation under the correspondence.
- Time:
- 10:00am-11:00am
- Description:
- Title: A tale of two groups - mapping class group and outer automorphism group of free group
Abstract: In this talk I will define two key groups studied in geometric
group theory - the mapping class group of a surface and the outer
automorphism group of a free group. I will discuss how the theory of
mapping class groups has motivated and guided the study of Out(F_n). Both groups act on certain hyperbolic simplicial complexes. For mapping class group these actions yield useful information about the group such as homological stability, finite asymptotic dimension, quasi-isometric rigidity. I will define some of these hyperbolic complexes and classifythe group elements that act with positive translation length.
- Time:
- 3:30pm
- Location:
- Ramanujan Hall
- Description:
- Title: Koszul Algebras 2