January 21, 2019 - January 25, 2019
Public Access Category: All |
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Maria Esteban
Affiliation: Universite Paris-Dauphine.
Time: 4pm, Wednesday, January 23.
Venue: Ramanujan Hall.
TITLE: Symmetry and symmetry breaking: rigidity and flows for PDEs and for
inequalities
ABSTRACT: In this talk, I will review recent results about how the use of
linear and nonlinear flows has been key to prove functional inequalities
and qualitative properties for their extremal functions. I will also
explain how from these inequalities and their best constants, optimal
spectral estimates can be obtained for Schrodinger operators. This is a
topic which is at the crossroads of nonlinear analysis and probability,
with implications in differential geometry and potential applications in
modelling in physics and biology.
- Time:
- 11:30am-1:00pm
- Location:
- A1A2 hall, CDEEP, IIT Bombay
- Description:
- Name of the instructor: Prof. Eduard Feireisl.
Affiliation: Czech Academy of Sciences.
Mode of instruction: via videoconference.
Title of the mini-course: Mathematical Aspects of Euler Equations.
Venue: A1A2 hall, CDEEP, IIT Bombay.
We consider the phenomenon of oscillations in the solution families to partial differential equations. To begin, we briefly discuss the mechanisms preventing oscillations/concentrations and make a short excursion in the theory of compensated compactness. Pursuing the philosophy "everything what is not forbidden is allowed" we show that certain problems in fluid dynamics admit oscillatory solutions. This fact gives rise to two rather unexpected and in a way contradictory results: (i) many problems describing inviscid fluid motion in several space dimensions admit global-in-time (weak solution); (ii) the solutions are not determined uniquely by their initial data. We examine the basic analytical tool behind these rather ground breaking results - the method of convex integration applied to problems in fluid mechanics and, in particular, to the Euler system.
- Time:
- 9:30am-11:00am
- Location:
- A1A2 hall, CDEEP, IIT Bombay
- Description:
- Name of the instructor: Prof. Eduard Feireisl.
Affiliation: Czech Academy of Sciences.
Mode of instruction: via videoconference.
Title of the mini-course: Mathematical Aspects of Euler Equations.
Venue: A1A2 hall, CDEEP, IIT Bombay.
We consider the phenomenon of oscillations in the solution families to partial differential equations. To begin, we briefly discuss the mechanisms preventing oscillations/concentrations and make a short excursion in the theory of compensated compactness. Pursuing the philosophy "everything what is not forbidden is allowed" we show that certain problems in fluid dynamics admit oscillatory solutions. This fact gives rise to two rather unexpected and in a way contradictory results: (i) many problems describing inviscid fluid motion in several space dimensions admit global-in-time (weak solution); (ii) the solutions are not determined uniquely by their initial data. We examine the basic analytical tool behind these rather ground breaking results - the method of convex integration applied to problems in fluid mechanics and, in particular, to the Euler system.
- Time:
- 11:30am-1:00pm
- Location:
- A1A2 hall, CDEEP, IIT Bombay
- Description:
- Name of the instructor: Prof. Eduard Feireisl.
Affiliation: Czech Academy of Sciences.
Mode of instruction: via videoconference.
Title of the mini-course: Mathematical Aspects of Euler Equations.
Venue: A1A2 hall, CDEEP, IIT Bombay.
We consider the phenomenon of oscillations in the solution families to partial differential equations. To begin, we briefly discuss the mechanisms preventing oscillations/concentrations and make a short excursion in the theory of compensated compactness. Pursuing the philosophy "everything what is not forbidden is allowed" we show that certain problems in fluid dynamics admit oscillatory solutions. This fact gives rise to two rather unexpected and in a way contradictory results: (i) many problems describing inviscid fluid motion in several space dimensions admit global-in-time (weak solution); (ii) the solutions are not determined uniquely by their initial data. We examine the basic analytical tool behind these rather ground breaking results - the method of convex integration applied to problems in fluid mechanics and, in particular, to the Euler system.
- Time:
- 3:30pm-5:00pm
- Location:
- Room No. 215 Department of Mathematics
- Description:
- Title : Introduction to Algebraic K Theory.
Speaker: Prof. Tony Puthenpurakal.
Time : 3:30 pm - 5 pm
Date : Friday 25 Jan 2019.
Venue : 215.