July 8, 2019 - July 12, 2019
Public Access Category: All |
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- Time:
- 3:00pm-4:00pm
- Location:
- Room No. 216 Department of Mathematics
- Description:
- Mathematics Colloquium Talk 1.
Speaker: Anisa Chorwadwala.
Affiliation: IISER Pune.
Date and Time: Wednesday 10 July, 3:00 pm - 4:00 pm.
Venue: Room 216, Department of Mathematics.
Title: A Glimpse of Shape Optimization Problems.
Abstract: The following questions arise quite naturally from what we see
around us. Why are soap bubbles that float in air approximately spherical?
Why does a herd of reindeer form a round shape when attacked by wolves? Of
all geometric objects having a certain property, which ones have the
greatest area or volume; and of all objects having a certain property,
which ones have the least perimeter or surface area? These problems have
been stimulating much mathematical thought. Mathematicians have been
trying to answer such questions and this has led to a branch of
mathematical analysis known as “shape optimisation problems”.
A typical shape optimisation problem is, as the name suggests, to find a
shape which is optimal in the sense that it minimises a certain cost
functional while satisfying given constraints. Isoperimetric problems form
a special class of shape optimisation problems. A typical isoperimetric
problem is to enclose a given area with a shortest possible curve. In
many cases, the functional being minimised depends on solution/s of a
given partial differential equation defined on a variable domain.
The plan is to give a glimpse of a few shape optimization problems we have
worked on.
- Time:
- 4:30pm-5:30pm
- Location:
- Room No. 216 Department of Mathematics
- Description:
- Mathematics Colloquium Talk 2.
Speaker: Apala Majumdar.
Affiliation: University of Bath.
Date and Time: Wednesday 10 July, 4:30 pm - 5:30 pm.
Venue: Room 216, Department of Mathematics.
Title: Solution Landscapes in the Landau-de Gennes Theory for Nematic
Liquid Crystals.
Abstract: Nematic liquid crystals are quintessential examples of soft
matter, intermediate in character between solids and liquids, with
long-range orientational order. We model spatio-temporal pattern formation
for nematic liquid crystals on two-dimensional polygonal geometries, which
are relevant for applications. We work within the powerful continuum
Landau-de Gennes theory for nematic liquid crystals. We illustrate the
complex solution landscapes on square domains as a function of the square
size, temperature and boundary conditions, reporting a novel Well Order
Reconstruction Solution on nnao-scale geometries. We discuss
generalizations to arbitrary 2D polygons, using symmetry-based and
variational techniques to study stable patterns in distinguished
asymptotic limits. We conclude by reviewing recent work on stabilization
of interior vortices by magneto-nematic coupling in ferronematics, which
leads to new possibilities for magneto-mechanical effects in nematic-based
materials. This is joint work with researchers in Peking University,
Shanghai Jiao Tong, IIT Delhi, IIT Bombay, Illinois Technological
University and University of Verona.
- Time:
- 4:00pm-5:00pm
- Location:
- Room 216, Department of Mathematics
- Description:
- Algebraic Geometry seminar.
Speaker: Mrinmoy Datta.
Affiliation: The Arctic University of Norway.
Date and Time: Thursday 11 July, 4:00 pm - 5:00 pm.
Venue: Room 216, Department of Mathematics.
Title: Bounds on the number of rational points on hypersurfaces defined
over finite fields.
Abstract: In this talk, we will revisit some of the known bounds on the
number of rational points on hypersurfaces of a given degree defined over
a finite field. We will recall a conjecture proposed by Homma and Kim
towards a tight upper bound on the number of rational points on a
nonsingular hyperface contained in an even dimensional projective space
over a finite field. Finally, we will present a recent work towards
proving the above mentioned conjecture for nonsingular threefolds
contained in a four-dimensional projective space.
- Time:
- 11:00am
- Location:
- Room No. 216 Department of Mathematics
- Description:
- Partial Differential Equations seminar.
Speaker: Sheetal Dharmatti.
Affiliation: IISER Thiruvananthapuram.
Date and Time: Friday 12 July, 11:00 am - 12:00 pm.
Venue: Room 216, Department of Mathematics.
Title: Data assimilation type Optimal control problem for Cahn Hilliard
Navier Stokes' system.
Abstract: This work is concerned about some optimal control problems
associated to the evolution of two isothermal, incompressible, immiscible
fluids in a two-dimensional bounded domain. The
Cahn-Hilliard-Navier-Stokes model consists of a Navier亡tokes equation
governing the fluid velocity field coupled with a convective Cahn蓬illiard
equation for the relative concentration of one of the fluids. A
distributed optimal control problem is formulated as the minimization of a
cost functional subject to the controlled nonlocal
Cahn-Hilliard-Navier-Stokes equations. We establish the first-order
necessary conditions of optimality by proving the Pontryagin maximum
principle for optimal control of such system via the seminal Ekeland
variational principle. The optimal control is characterized using the
adjoint variable. We also study another control problem which is similar
to that of data assimilation problems in meteorology of obtaining unknown
initial data using optimal control techniques when the underlying system
is same as above.
- Time:
- 12:00pm-1:00pm
- Location:
- Room No. 216 Department of Mathematics
- Description:
- Partial Differential Equations seminar
Speaker: Utpal Manna.
Affiliation: IISER Thiruvananthapuram.
Date and Time: Friday 12 July, 12:00 pm - 1:00 pm.
Venue: Room 216, Department of Mathematics.
Title: Weak Solutions of a Stochastic Landau豊ifshitz萌ilbert Equation
Driven by Pure Jump Noise.
Abstract: In this work we study a stochastic three-dimensional
Landau-Lifschitz-Gilbert equation perturbed by pure jump noise in the
Marcus canonical form. We show existence of weak martingale solutions
taking values in a two-dimensional sphere $S^2$ and discuss certain
regularity results. The construction of the solution is based on the
classical Faedo-Galerkin approximation, the compactness method and the
Jakubowski version of the Skorokhod Theorem for nonmetric spaces. This is
a joint work with Zdzislaw Brzezniak (University of York) and has been
published in Commun. Math. Phys. (2019),
https://doi.org/10.1007/s00220-019-03359-x.