Abstract: Over the last decade, a Brill-Noether theory for tropical curves
analogous to the corresponding theory for algebraic curves has taken
shape.
This was discussed by Ashwin Deopurkar in the first few
CACAAG talks. I will sketch the proof of the nonexistence part of the
Brill-Noether theorem for tropical curves. This is based on the paper ``A
tropical proof of the Brill-Noether Theorem'' by Cools,Draisma,Payne and
Robeva.
Time:
11:30am-1:00pm
Location:
Room No. 215, Department of Mathematics
Description:
Commutative algebra seminar
speaker: H. Ananthnarayan
Venue: MA 215
Date:April 3
Time: 11.30-1.00
Title: Monomial Basis of a Quotient Ring
Abstract: A polynomial ring S over a field k has a basis consisting of
monomials. Given a quotient ring R of S, one would like to identify the
monomials whose images form a k-basis of R. We will discuss the ideas of a
monomial order, and initial ideals, leading to Groebner basis, which help
answer this question.
Time:
4:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Mathematics Colloquium
Date & Time: 4th April, 2018 at 4pm
Venue: Ramanujan Hall
Speaker: Manoj Gopalkrishnan
Title: Imagining how a cell thinks: The design of reaction network schemes
that do machine learning
Abstract: A living cell responds in sophisticated ways to its environment.
Such behavior is all the more remarkable when one considers that a cell is
a bag of molecules. A detailed algorithmic explanation is required for how
a network of chemical reactions can produce sophisticated behavior. Several
previous works have shown that reaction networks are computationally
universal and can, in principle, implement any algorithm. The problem is
that these constructions have not mapped well onto biological reality, have
made wasteful use of the computational potential of the native dynamics of
reaction networks, and have not made any contact with statistical
mechanics. We seek to address these problems.
We find that the mathematical structure of reaction networks is
particularly well suited to implementing modern machine learning
algorithms. We describe a new reaction network scheme for solving a large
class of statistical problems including the problem of how a cell would
infer its environment from receptor-ligand bindings. Specificially we show
how reaction networks can implement information projection, and
consequently a generalized Expectation-Maximization algorithm, to solve
maximum likelihood estimation problems in partially-observed exponential
families on categorical data. Our scheme can be thought of as an
algorithmic interpretation of E. T. Jaynes's vision of statistical
mechanics as statistical inference.
Time:
2:00pm-3:30pm
Location:
Room No. 105, Department of Mathematics
Description:
PDE seminar
Date and Time: April 5, Thursday, 2-3:30 p.m.
Venue: Room 105, Mathematics Department
Title: Control of infinite dimensional linear systems
Speaker: Dr. Debanjana Mitra,
Abstract: First, we recall semigroup theory. Using this, we study the
controllability and stabilizability of linear partial differential
equations. In details, th