Date and Time: Monday 08 April, 7:30 pm - 8:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Tensors and Syzygies.
Abstract: Tensors are higher dimensional analogues of matrices. But unlike
matrices, there is still so much we don't know about their fundamental
algebraic properties. For example, for rank-r matrices we know that the
determinants of all (r+1)-minors of the matrix furnish a generating set
for the ideal of all relations among the entries of such matrices, but for
general rank-r tensors we have almost no idea what polynomials generate
their ideals. Moreover the entire minimal free resolution of the ideal in
the matrix case is know in terms of representation theory (Lascoux,
Eagon-Northocott, Weyman, and others), but relatively little is known in
the tensor case, (not even the length of the resolution).
I'll present evidence toward a conjecture on arithmetic
Cohen-Macaulay-ness that would generalize the Eagon-Hochster result in the
matrix case. I'll also highlight recent work with Raicu and Sam where we
compute precise vanishing and non-vanishing of the syzygies of rank-1
tensors.
Time:
11:30am-12:30pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Combinatorics and Theoretical Computer Science seminar.
Speaker: Rahul Santhanam.
Affiliation: University of Oxford.
Date and Time: Tuesday 09 April, 11:30 am - 12:30pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Independence Results in Propositional Proof Complexity.
Abstract: Given the lack of progress on complexity lower bounds, it is
natural to ask whether they are hard to prove, in some formal sense. I
will begin by briefly describing the classical incompleteness results of
Godel and Chaitin, and posing the question for whether there are analogues
of these results in complexity theory.
I will then introduce the finitistic framework of propositional proof
complexity, where we are interested in the existence of polynomial size
proofs verifiable in polynomial time. I will explain what it means to
prove circuit complexity or proof complexity lower bounds in this
framework. Finally, I will describe a strong complexity conjecture for
which it can be shown unconditionally that there are no feasible
propositional proofs, in a certain technical sense.
Time:
2:30pm-3:30pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Geometry and Topology Seminar.
Speaker: Shuddhodan.
Affiliation: Freie Universitat, Berlin.
Date and Time: Tuesday 09 April, 2:30 pm - 3:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Self maps of varieties over finite fields.
Abstract: Esnault and Srinivas proved that as in de Rham cohomology over
the complex numbers, the value of the entropy of an automorphism of a
smooth proper surface over a finite field $\F_q$ is taken in the span of
the Neron-Severi group inside of of $\ell$-adic cohomology. In this talk
we will discuss some analogous questions in higher dimensions motivated by
their results and techniques.
Time:
3:30pm-5:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Algebraic K-Theory Seminar.
Speaker: Manoj Keshari.
Date and Time: Friday 12 April, 3:30 pm - 5:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: K_0 of an exact category (3rd lecture).
Time:
5:15pm-6:30pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
CACAAG Seminar.
Speaker: Madhusudan Manjunath.
Date and Time: Friday 12 April, 5:15 pm - 6:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Lorenzini Zeta Function of a Graph.
Abstract: We will see a two variable zeta function associated with a graph
due to Dino Lorenzini. I will mainly spend time discussing divisor theory
on graphs that arises in the definition of this zeta function.