April 15, 2019 - April 19, 2019
Public Access Category: All |
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- 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.