Abstract: This is the first in a series of lectures on class field theory.
We begin with Chapter 1 in Cassels and Frohlich.
Time:
4:00pm-5:00pm
Location:
Ramanujan Hall
Description:
Title: Extension and Regularity of CR Functions near CR Singularities
Abstract:
CR functions are certain generalizations of holomorphic functions and CR
manifolds are those that support CR functions. For instance, a
pseudoconvex hypersurface in $\mathbb{C}^N$ is a CR manifold and CR
functions are locally boundary values of holomorphic functions. We will
begin by describing this holomorphic extension result before proceeding to
discuss the codimension two case. Codimension two submanifolds of
$\mathbb{C}^N$ generically have isolated CR singularities and we are
interested in studying the behaviour of the extension of CR functions near
CR singularities. We prove that under certain nondegeneracy conditions on
the CR singularity this extension is smooth up to the CR singularity. This
is joint work with Jiri Lebl and Alan Noell.
Time:
11:30am-12:30pm
Location:
Ramanujan Hall
Description:
Title: Uncertain Compression and Graph Coloring
Speaker: Madhu Sudan (Harvard)
The classical task of compression, made famous by the works of Shannon and
Huffman, asks the question: Given a distribution on possible messages, how
can one build a dictionary to represent the messages so as to
(approximately) minimize the expected length of the representation of a
random message sampled from this distribution. Given the centrality of
compression as a goal in all, natural or designed, communication, we
introduce and study the uncertain compression problem. Here the goal is to
design a compression scheme that associates a dictionary to each
distribution such that messages can be recovered even by receivers that do
not know the distribution exactly, but only know them approximately.
Understanding the limits of uncertain compression leads to intriguing
challenges and in particular leads to the challenge of understanding the
chromatic number of an explicit family of graphs. In this talk we will
describe some of the graphs, and attempts to bound their chromatic number.
Based on joint works with Badih Ghazi, Elad Haramaty, Brendan Juba, Adam
Kalai, Pritish Kamath and Sanjeev Khanna.
Time:
2:30pm
Location:
Ramanujan Hall
Description:
Speaker: Akshaa Vatwani, University of Waterloo
Title : Variants of equidistribution in arithmetic progressions
Abstract: It is well known that the prime numbers are equidistributed in
arithmetic progressions. Such a phenomenon is also observed more generally
for a class of multiplicative functions. We derive some variants of such
results and give a few applications. We also discuss an interesting
application that relates to the Chowla conjecture on correlations of the
Mobius function, and show its relevance to the twin prime conjecture.
Time:
3:30pm-5:30pm
Location:
Room 215, Department of Mathematics
Description:
Speaker: Prof. Mahan Mj (TIFR Mumbai)
Title: Non-arithmetic lattices
Abstract: We shall describe a construction of non-arithmetic lattices in SO(n,1)
following Agol.