10:30am» Anupam Kumar Singh, IISER Pune- Time:
- 10:30am - 12:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Algebraic Groups Seminar.
Speaker: Anupam Kumar Singh.
Affiliation: IISER Pune.
Date and Time: Monday 01 April, 10:30 am - 12:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: On Shalev's conjecture for type A_n and {}^2A_n.
Abstract: Let G be a group and w a word map on G. Shalev and others
computed bounds for |w(G)|/|G| when G is a finite simple group of Lie type
and showed that the lower bound is c/n except for type A_n and {}^2A_n. He
further conjectured that the same bound is expected for these cases as
well. In this talk, we present our exploration in this direction
- Time:
- 3:30pm - 4:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Statistics Seminar.
Speaker: Ujjwal Das.
Affiliation: IIM Udaipur, Rajasthan.
Date and Time: Tuesday 02 April, 3:30 pm - 4:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Inference on zero inflated ordinal models with semiparametric link.
Abstract: In socioeconomic and Biological studies, observations on
individuals are often observed longitudinally on a Likert-type scale with
substantially large proportion of zeros. This leads to a special case of
mixture structured data where extra-variation occurs. Obviously the
standard ordinal data analysis fails to provide appropriate statistical
inference. We propose a suitable zero inflated semi parametric ordinal
model that takes into account the non linear link between the ordinal
response and a covariate. A sieve maximum likelihood estimator(MLE) is
proposed for the regression parameter of interest. We also propose a test
for the zero proportion in this semi parametric model. A simulation study
has been carried out to investigate the performance of the estimator as
well as the test.
- Time:
- 3:00pm - 3:50pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Popular Talk.
Speaker: Harsha Hutridurga.
Date and Time: Wednesday 03 April, 3:00 pm - 3:50 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Intrigue of Invisibility cloaking.
Abstract: Rendering objects or oneself invisible to others has fascinated
us since the dawn of human civilization. Illustration of such vanishing
acts are often made in sci-fi movies. Even though this idea of making
oneself invisible to others sounds out of reach, lately it is gaining
traction in the scientific community. This has led to the emergence of a
fascinating field of meta-materials which deals with the design and study
of assemblies of ordinary materials such that the assembly as a whole
behaves in an exotic manner. This talk will try to present some elementary
ideas involved in the theory of invisibility cloaking. The talk is
intended for non-experts and will be accessible to people familiar with
basic notions in multivariable calculus.
- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Department Colloquium.
Speaker: Rachel Kuske.
Affiliation: Georgia Tech.
Date and Time: Wednesday 03 April, 4:00 pm - 5:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Prevalence of heavy-tailed distributions in systems with multiple
scales: insights through stochastic averaging.
Abstract: Heavy tailed distributions have been shown to be consistent with
data in a variety of systems with multiple time scales. Recently,
increasing attention has appeared in different phenomena related to
climate. For example, correlated additive and multiplicative (CAM)
Gaussian noise, with infinite variance or heavy tails in certain parameter
regimes, has received increased attention in the context of atmosphere
and ocean dynamics. We discuss how CAM noise can appear generically in
many reduced models. Then we show how reduced models for systems driven by
fast linear CAM noise processes can be connected with the stochastic
averaging for multiple scales systems driven by alpha-stable processes. We
identify the conditions under which the approximation of a CAM noise
process is valid in the averaged system, and illustrate methods using
effectively equivalent fast, infinite-variance processes. These
applications motivate new stochastic averaging results for systems with
fast processes driven by heavy-tailed noise. We develop these results for
the case of alpha-stable noise, and discuss open problems for identifying
appropriate heavy tailed distributions for these multiple scale systems.
This is joint work with Prof. Adam Monahan (U Victoria) and Dr. Will
Thompson (UBC/NMi Metrology and Gaming).
- Time:
- 3:30pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Algebraic K-Theory Seminar.
Speaker: Manoj Keshari.
Date and Time: Friday 05 April, 3:30 pm - 5:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: K_0 of a ring (2nd lecture).
- Time:
- 5:15pm - 6:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG Seminar.
Speaker: Madhusudan Manjunath.
Date and Time: Friday 05 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.
- Time:
- 7:30pm - 8:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- IITB Mathematics Colloquium via videoconference.
Speaker: Luke Oeding.
Affiliation: Auburn University.
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.
- Time:
- 10:30am - 12:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Lecture Series on Partial Differential Equations.
Speaker: Kirill Cherednichenko.
Affiliation: University of Bath.
Title: Periodic PDEs with micro-resonators: unified approach to
homogenisation and time-dispersive media.
Venue: Ramanujan Hall, Department of Mathematics.
Date and Time: Tuesday 16 April, 10.30 am - 12.30 pm
Lecture I:
An overview of the mathematical theory of homogenisation as a toolbox for the analysis of multiscale problems. Wave propagation: resonant and nonresonant regimes. Non-resolvent estimates, time dispersion, and metamaterials: amotivation for a novel homogenisation principle.
- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Geometry and Topology Seminar.
Title : Grothendieck's theorem on algebraic de Rham cohomology of
varieties
Speaker: Saurav Bhaumik
Time & Date: 4-5pm, Tuesday 16th April.
Venue: Ramanujan Hall.
Abstract: Let X be a smooth scheme of finite type over C, and let X' be
the corresponding complex analytic variety. Grothendieck proved that the
complex cohomologies H^q(X') can be calculated as the hypercohomologyes of
the algebraic de Rham complex on X. We will present Grothendieck's proof.
- Time:
- 5:10pm - 6:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Popular Talk in Mathematics.
Speaker: Atharva Korde.
Date and Time: Tuesday, 16 April. 5.10 pm - 6.00 pm.
Refreshments will be served before the talk.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Secret avatars of two spaces.
Abstract: The spaces SL(2, R) and SL(2,R)/SL(2, Z) look quite difficult to
visualize at first glance. In this talk, we shall see that these two
spaces are actually homeomorphic to some nice-looking spaces.
- Time:
- 10:30am - 12:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Lecture Series on Partial Differential Equations.
Speaker: Kirill Cherednichenko.
Affiliation: University of Bath.
Title: Periodic PDEs with micro-resonators: unified approach to
homogenisation and time-dispersive media.
Venue: Ramanujan Hall, Department of Mathematics.
Wednesday 17 April, 10.30 am - 12.30 pm
Lecture II.
Spectral boundary-value problems: boundary triples and the corresponding M-operators (“Dirichlet-to-Neumann maps”). Their role in the quantitative analysis of degenerate problems. Krein formula for a generalised Robin problem.
- Time:
- 10:00am - 12:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Lecture Series on Partial Differential Equations.
Speaker: Kirill Cherednichenko.
Affiliation: University of Bath.
Title: Periodic PDEs with micro-resonators: unified approach to
homogenisation and time-dispersive media.
Venue: Ramanujan Hall, Department of Mathematics.
Thursday 18 April, 10.00 am - 12.00 pm
Lecture III:
Periodic media with resonant components (“high contrast composites”). Gelfand transform and direct integral: a reduction of the full-space problem
to a family of “transmission” problems on the period cell. A reformulation in terms
of the M-operator on the interface. Diagonalisation of the M-operator on the nonresonant component: Steklov eigenvalue problem.
- Time:
- 5:15pm - 6:15pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar.
Speaker: Priyamvad Srivastav.
Affiliation: IMSc, Chennai.
Date and Time: Thursday 18 April, 5.15 pm - 6.15 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Product of primes in arithmetic progression.
Abstract: Let $q$ be a positive integer and let $(a,q)=1$ be a given
residue class. Let $p(a,q)$ denote the least prime congruent to $a
\mod{q}$. Linnik's theorem tells us that there is a constant $L>0$, such
that the $p(a,q) \ll q^L$. The best known value today is $L = 5.18$.
A conjecture of Erdos asks if there exist primes $p_1$ and $p_2$, both
less than $q$, such that $p_1 p_2 \equiv a \mod{q}$. Recently, Ramar\'{e}
and Walker proved that for all $q \geq 2$, there are primes $p_1, p_2,
p_3$, each less than $q^{16/3}$, such that $p_1 p_2 p_3 \equiv a \mod{q}$.
Their proof combines additive combinatorics with sieve theoretic
techniques. We sketch the ideas involved in their proof and talk about a
joint work with Olivier Ramar\'{e}, where we refine this method and obtain
an improved exponent of $q$.
- Time:
- 10:30am - 12:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Lecture Series on Partial Differential Equations.
Speaker: Kirill Cherednichenko.
Affiliation: University of Bath.
Title: Periodic PDEs with micro-resonators: unified approach to
homogenisation and time-dispersive media.
Venue: Ramanujan Hall, Department of Mathematics.
Friday 19 April, 10.30 am - 12.30 pm.
Lecture IV.
Schur-Frobenius inversion formula the generalised resolvent on the
resonant inclusion. An effective description of the original family of transmission
problems. A time-dispersive effective formulation in the whole space. An example
of the effective formulae for a specific cell geometry. Band gaps and “metamaterial”
properties.
- Time:
- 2:30pm - 3:30pm
- Location:
- Room No. 113, Department of Mathematics
- Description:
- Commutative algebra:
Date, Time, Venue: Friday, 19th Apr, 2:30 - 3:30 p.m.,Commutative algebra Room 113.
Title: Pure modules and Cohen-Macaulay rings
Abstract: This is a talk in Boij-Soderberg theory, which involves the
study of Betti cones over quotients of polynomial rings. These were
introduced by Boij-Soderberg in 2008, and explored further by
Eisenbud-Schreyer in 2009. I will give a quick introduction to this theory
and the main problems.
Finally, I will point out how of a result of mine (joint with Rajiv
Kumar) on the construction of pure modules over Cohen-Macaulay rings
follows immediately from the work of Eisenbud-Schreyer using Noether
Normalization, and the Auslander-Buchsbaum Formula (which are two
important results the students proved in the reading course).
I will try to make the talk as self-contained as possible. All are welcome.
- Time:
- 9:00am - 10:15am
- Location:
- Room No. 114, Department of Mathematics
- Description:
- Time: 9.00 am - 10.15 am.
Speaker: R.V. Gurjar.
Title: Linquan Ma’s generalisations of Lech’s Conjecture
Abstract: The following two results will be considered. Let (A,M) ⊂ (R,N) be a local flat homomorphism with A a regular local ring such that A contains its residue field. Let I be an ideal in A. Then eR/IR ≥ eR, where e denotes the multiplicity. Ma has stated four conjectures related to Lech’s Conjecture. We will discuss the relationships between these conjectures. If time permits, I will indicate how we can understand C.P. Ramanujam’s geometric interpretation of multiplicity in a more intuitive manner.
- Time:
- 10:15am - 11:30am
- Location:
- Room No. 114, Department of Mathematics
- Description:
- Time:10.15 am - 11.30 am.
Speaker: Sudeshna Roy
Title: Linquan Ma’s solution of the cyclic generalised Lech’s conjecture for graded rings
Abstract: Let R be a standard graded K-algebra and I be a homogeneous ideal. In this talk we show that if pdRR/I < ∞, then eR | eR/I. In particular, eR ≤ eR/I.
- Time:
- 11:45am - 1:00pm
- Location:
- Room No. 114, Department of Mathematics
- Description:
- Time: 11.45 am - 01.00 pm.
Speaker: Kriti Goel.
Title: Numerically Robert rings.
- Time:
- 2:30pm - 3:45pm
- Location:
- Room No. 114, Department of Mathematics
- Description:
- Time: 02.30 pm - 03.45 pm.
Speaker: Mitra Koley.
Title: Lech’s conjecture for 3-dimensional Gorenstein rings
Abstract for (3) and (4): Ma formulated a weakened generalised Lech’s conjecture and proved it for a class of rings known as numerically Roberts rings, in equal characteristic p > 0. Using these results, combined with results on Hilbert-Kunz multiplicities, he proved the Lech’s conjecture for 3-dimensional Gorenstein rings of equal characteristic p > 0. In the first part of the talk, we define numerically Roberts rings and prove a few results required for proving the main result, which will be proved in the second part of the talk.
- Time:
- 4:00pm - 5:15pm
- Location:
- Room No. 114, Department of Mathematics
- Description:
- Time: 4.00 pm - 5.15 pm.
Speaker: Shreedevi Masuti.
Title: The Stru¨ckrad-Vogel conjecture
Abstract: Let M be a finite module of dimension d over a Noetherian local ring (R,m). The set{`(M/IM)/e(I,M)}, where I varies over m-primary ideals, is bounded below by (1/d!)e(R/textannM). If ˆ M is equidimensional, this set is bounded above by a constant depending only on M. The lower bound extends an inequality of Lech and the upper bound answers a question of Stru¨ckrad-Vogel.