Speaker: Atharva Korde
Title: Cartan's theory of the highest weight and Verma modules
Day and Date: Monday, August 20
Time: 15:30 - 17:00
Venue: Room Ramanujan Hall, 2nd floor, Department of Mathematics
Abstract: Finite dimensionality of Verma modules and the Weyl character
formula.
Time:
5:15pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Popular Lecture in Mathematics
Date & Time: Monday 20th August 2018 at 5:15 PM.
Venue: Ramanujan Hall
Speaker: Venkitesh Iyer
Title: A Fixed Point Theorem and a Coloring Lemma
Abstract: The Sperner Lemma is a combinatorial lemma that talks about a
certain type of coloring (called the Sperner coloring) of a triangulation
of a simplex. It has applications in several root-finding and
fair-division algorithms.
The Brouwer Fixed Point Theorem is a classical theorem that asserts the
existence of a fixed point for a continuous function from the unit disc in
Euclidean space to itself.
There are several proofs for each of these results. In this talk, we will
show that both these results are equivalent. We will look at the proof in
the case of two dimensions. The general case is similar modulo some more
careful book-keeping.
[We encourage all MSc, Ph.D and UG students to attend. Note tea and
snacks will be served before the talk at 5:00 PM.]
Time:
3:30pm-4:30pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Mathematics Colloquium
Date & Time : Tuesday 3:30-4:30pm
Venue: Ramanujan Hall
Speaker: Saurabh Kumar Singh
Title: Sub-convexity problems: Some history and recent developments
Abstract : attached.
Time:
5:00pm-6:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Seminar: CACAAG.
Lecture 1: Time: 5-6 pm, Tuesday, August 21, 2018.
Venue: Ramanujan Hall.
Speaker: J. K. Verma
Title: Richard Stanley's solution of Anand-Dumir-Gupta conjecture about
enumeration of magic squares
Abstract: In 1973 Richard Stanley solved several conjectures about magic
squares
proposed by Harsh Anand, V. C. Dumir and Hans Raj Gupta. In his "Green
Book"
Stanley used the theory of Cohen-Macaulay and Gorenstein rings to solve
these
conjectures. I will sketch his solution assuming only basic commutative
algebra.
Time:
6:00pm-7:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Lecture 2: Time: 6-7 pm, Tuesday, August 21, 2018.
Venue: Ramanujan Hall.
Speaker: Suchita Goyal
Title: Neighborhood Complexes of Graphs
Time:
2:00pm-3:30pm
Location:
Room No. 215, Department of Mathematics
Description:
Commutative algebra seminar
Speaker: Sudeshna Roy
Title: Equations of multi-Rees algebra of a family of monomial ideals
Venue: Room 215
Date and Day: Thursday, 23 August, 2018
Time: 2-3.30 PM
Abstract: Consider the the multi-Rees algebra \R_R(I_1 \oplus \cdots \oplus
I_r)
of monomial ideals I_1, . . . , I_r. In this talk, the defining ideal of
\R_R(I_1 \oplus \cdots \oplus I_r)
will be described explicitly. We will cover Section 1 and Section 2 of the
recent paper
"Multi-Rees Algebras and Toric Dynamic Systems" (
https://arxiv.org/pdf/1806.08184.pdf)
of Cox, Lin and Sosa. We will also see that for any homogeneous ideals J_1,
. . . , J_s,
the defining ideal of \R_R(J_1 \oplus \cdots \oplus J_s) can be expressed
as a contraction
of the defining ideal of \R_R(I_1 \oplus \cdots \oplus I_r) for some
monomial ideals I_1, . . . , I_r.
Time:
4:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Date & Time: Friday, 24th August, 4pm
Venue: Ramanujan Hall
Speaker: Dr Richard Clarke, Associate Dean Post Graduate Research,
Engineering department from the University of Auckland
Title: Active Matter: A smart material for the 21st Century
Abstract: The theories of fluid dynamics and solid mechanics are a
cornerstone of Engineering, enabling us to make predictions about the way
in which materials and structures behave. The continuum-level mathematical
formulations which were developed over a century ago allow us to overcome
the impracticalities of considering every microscopic particle within the
system, and instead consider the materialâ€™s macroscopic bulk behaviour. The
type of substances usually described in this way are passive, meaning that
the drivers of the system are usually externally-applied forces or energy.
However, there exist more exotic types of active matter, where the
constituent components themselves contain a source of energy. Suspensions
of swimming microbes provide an important example. The innumerable cells
within the mixture are capable of self-propelling themselves through the
suspending medium. Modern micro- and nano-fabrication methods also allow
for the creation of artificial microswimmers. The flows generated by
self-motile cells leads to fluid-mediated coupling between the swimmers,
which can lead to highly-organised collective bulk motions, sometimes
referred to as bacterial turbulence or slow turbulence. This
self-organisation has also be seen to change the bulk rheology of the
suspension, leading to plastic and superfluidic behaviours, some of which
may have technological applications. Continuum models developed for passive
materials do not perform well for active matter, and so there has been a
great deal of interest and interdisciplinary activity in recent years to
derive an effective continuum-level description for such systems. In this
talk I will outline some of the current challenges, as well as ideas and
progress made to-date in this area.
Time:
4:00pm
Location:
Room No. 215, Department of Mathematics
Description:
Geometry and Topology seminar
Speaker: Reebhu Bhattacharya
Date & Time : 24th August at 4: 00 PM
Venue: Room 215
Title: Towards Jones Isomorphism Theorem: Preliminaries(Intersection theory, Morse theory and Hochschild Complex)
Abstract:
I will be talking about three distinct topics which will serve as preliminaries for the Jones isomorphism theorem which we will discuss in a later talk. Firstly we will talk about some intersection theory and prove the Thom isomorphism theorem. Finally we will define the Hochschild complex for differential graded algebras and it's Hochschild (co) homology.