Speaker: Dr. Ayan Bhattacharya
Researcher in Stochastics
CWI, Amsterdam.
Time: 4 pm, Tuesday, 8th January.
Venue: Ramanujan Hall.
Title: Large deviation for extremes in branching random walk
Abstract:
We shall consider branching random walk with displacements having
regularly varying tails. Extreme positions of particles are very
important to study in the context of statistical physics, computer
science, probability and biology. Point process is the best known tool in
extreme value theory to study joint asymptotic behavior of extremes.
In this talk, we shall focus on large deviation results for point
processes arising in the above mentioned model.
Time:
4:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Speaker: Prof. Ramesh Gangoli, University of Washington.
Time: 4pm, Wednesday, 9th January.
Venue: Ramanujan Hall.
Title: Some unpublished work of Harish-Chandra.
Abstract:
When Harish-Chandra died in 1983, he left behind a voluminous pile of
handwritten manuscripts on harmonic analysis on semisimple Lie groups over
real/complex and p-adic fields. The manuscripts were turned over to the
archives of the Institute for Advanced Study at Princeton, and are
archived there.
Robert Langlands is the Trustee of the Harish- Chandra archive, and has
always been interested in finding a way of salvaging whatever might be
valuable in these manuscripts. Some years ago, at a conference in UCLA, he
asked if V. S. Varadarajan and I might look at some of these.
The results of our efforts have resulted in the publication of the Volume
5 (Posthumous) of the Collected works of Harish-Chandra by Springer
Verlag.
My talk will be devoted to a bare outline of the results in this volume,
without much detail, but I will try to convey some information about the
key method used in the work.
Time:
11:00am
Location:
Ramanujan Hall, Department of Mathematics
Description:
Speaker: Dr. Mrinal Kumar, Simons Institute for the Theory of Computing,
Berkeley, USA.
Time: 11 am, Friday, 11th January.
Venue: Ramanujan Hall.
Title : Some closure results for polynomial factorization and applications
Abstract : In a sequence of seminal results in the 80's, Kaltofen showed
that if an n-variate polynomial of degree poly(n) can be computed by an
arithmetic circuit of size poly(n), then each of its factors can also be
computed an arithmetic circuit of size poly(n). In other words,
the complexity class VP (the algebraic analog of P) of polynomials, is
closed under taking factors.
A fundamental question in this line of research, which has largely
remained open is to understand if other natural classes of
multivariate polynomials, for instance, arithmetic formulas, algebraic
branching programs, constant depth arithmetic circuits or the
complexity class VNP (the algebraic analog of NP) of polynomials, are
closed under taking factors. In addition to being fundamental
questions on their own, such 'closure results' for polynomial
factorization play a crucial role in the understanding of hardness
randomness tradeoffs for algebraic computation.
I will talk about the following two results, whose study was motivated
by these questions.
1. The class VNP is closed under taking factors. This proves a
conjecture of B{\"u}rgisser.
2. All factors of degree at most poly(log n) of polynomials with
constant depth circuits of size
poly(n) have constant (a slightly larger constant) depth arithmetic
circuits of size poly(n).
This partially answers a question of Shpilka and Yehudayoff and has
applications to hardness-randomness tradeoffs for constant depth
arithmetic circuits. Based on joint work with Chi-Ning Chou and Noam
Solomon.