Speaker: Professor Vydas Cekanavicius
Vilnius University
Lithuania
Title: Infinitely Divisible Approximations for Sums of Markov-Dependent RVs.
Abstract:
We demonstrate that for discrete Markov dependent rvs, the normal approximation can be effectively replaced by compound Poisson approximation..In case of three
state Markov chain, the effect of symmetry will be estimated.
Time:
2:30pm-3:30pm
Location:
Ramanujan Hall
Description:
Title: Jimm, a fundamental involution
Abstract: Dyer's outer automorphism of PGL(2,Z) induces an involution
of the real line, which behaves very much like a kind of modular
function. It has some striking properties: it preserves the set of
quadratic irrationals sending them to each other in a non-trivial way
and commutes with the Galois action on this set. It restricts to an
highly non-trivial involution of the set unit of norm +1 of quadratic
number fields. It conjugates the Gauss continued fraction map to the
so-called Fibonacci map. It preserves harmonic pairs of numbers
inducing a duality of Beatty partitions of N. It induces a subtle
symmetry of Lebesgue's measure on the unit interval.
On the other hand, it has jump discontinuities at rationals though its
derivative exists almost everywhere and vanishes almost everywhere. In
the talk, I plan to show how this involution arises from a special
automorphism of the infinite trivalent tree
Time:
4:00pm
Location:
Ramanujan Hall
Description:
Title: Tropical Algebraic Geometry: an Introduction.
Tropical algebraic geometry is in the interface of algebraic and polyhedral geometry with applications to both these topics. We start with a gentle introduction to tropical algebraic geometry. We then focus on the tropical lifting problem and discuss recent progress. Tropical analogues of graph curves play an important role in this study.
Please note:
1. Dr. Manjunath is a faculty candidate.
2. The talk will be via skype
Time:
11:00am-12:30pm
Location:
Room No. 216
Description:
Title: Rational Singularities VI
Time:
11:00am-12:00pm
Location:
Ramanujan Hall
Description:
Title: Recent developments on the Sunflower conjecture
Abstract: A sunflower with p petals is a family of sets A_1,...,A_p
such that the intersections of all pairs of distinct sets are the
same. A famous conjecture in combinatorics, called the Sunflower
conjecture, asserts a bound on the maximum size of any family of
k-sets that does not contain a p-sunflower. We review some recent work
by Ellenberg-Gijswijt and Naslund-Swain that proves a weak variant of
this conjecture due to Erdos and Szemeredi.
Time:
4:00pm-5:00pm
Location:
Ramanujan Hall
Description:
Speaker: Willem H. Haemers
Tilburg University, The Netherlands
Title: Are almost all graphs determined by their spectrum?
Abstract: An important class of problems in mathematics deals with the reconstruction of a
structure from the eigenvalues of an associated matrix. The most famous such prob-
lem is: ‘Can one hear the shape of a drum?’. Here we deal with the question: ‘Which
graphs are determined by the spectrum (eigenvalues) of its adjacency matrix’? More
in particular we ask ourselves whether this is the case for almost all graphs. There
is no consensus on what the answer should be, although there is a growing number
of experts that expect it to be affirmative. In this talk we will present several re-
sults related to this question. This includes constructions of cospectral graphs and
characterizations of graphs by their spectrum. Some of these results support an
affirmative answer, some support the contrary. It will be explained why the speaker
believes that it is true.
Time:
5:00pm-6:30pm
Location:
Room No. 215
Description:
Title: Some consequences of the Riemann hypothesis for varieties over
finite fields - II
Abstract: We will talk about a result of M. Katz and W. Messing, which
says the following. From the Riemann hypothesis and the hard Lefschetz
theorem in l-adic cohomology, the corresponding facts for any Weil
cohomology follow.
Time:
3:00pm-5:00pm
Location:
Room No. 215
Description:
Title: Finiteness of homotopy groups of spheres
Abstract:
In this talk I will prove that the i-th homotopy groups of a sphere S^n are finite when i is greater than n, except in one particular case, using the Serre spectral sequence. In the first half of the talk I will give the background material needed to understand the proof.
Time:
3:30pm
Location:
Ramanujan Hall
Description:
Title: Ideals of Linear Type I
Abstract: In this talk, we study the basics of defining ideal of the Rees algebra of Ideal I and what makes the ideal to be of linear type. Further, we prove that ideals generated by a regular sequences are of linear type.