8:00am 


9:00am 
[9:30am] Prof. Eduard Feireisl, Czech Academy of Sciences
 Description:
 Name of the instructor: Prof. Eduard Feireisl.
Affiliation: Czech Academy of Sciences.
Mode of instruction: via videoconference.
Title of the minicourse: 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 globalintime (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.


10:00am 

11:00am 
[11:00am] Dilip Patil
 Description:
 Commutative Algebra Seminar
Speaker: Dilip Patil.
Time & Date: 11:00 a.m.  12:30 p.m., Wednesday, 30th Jan 2019.
Venue: Room 215.
Title: Some Questions on HilbertSamuel functions.
[11:30am] Prof. Eduard Feireisl, Czech Academy of Sciences
 Description:
 Name of the instructor: Prof. Eduard Feireisl.
Affiliation: Czech Academy of Sciences.
Mode of instruction: via videoconference.
Title of the minicourse: 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 globalintime (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.


12:00pm 

1:00pm 


2:00pm 
[2:00pm] Dipendra Prasad
 Description:
 Lecture Series
Speaker: Dipendra Prasad.
Time: 2pm (3:30pm), Wednesday, 30 January 2019.
Venue: Room 216.
Title: An introduction to Lie groups, Symmetric spaces, and Shimura
varieties based on examples".
Abstract: I will give an introductory course of 34 lectures on the topics
mentioned in the title to an audience without any prior knowledge of the
subject which is a meeting ground for Differential geometry, Algebraic
geometry, and Number theory.


3:00pm 

4:00pm 
[4:00pm] Mathematics Colloquium
 Description:
 Mathematics Colloquium
Speaker: Aditya Karnataki, Beijing International Center for Mathematical
Research
Date: Wednesday, 30 January 2019.
Time: 4:005:00pm.
Venue: Ramanujan Hall.
Title  Finiteness of cohomology of arithmetic families of $(\varphi,
\Gamma)$modules.
Abstract  We will explain constructions of Robba rings and $(\varphi,
\Gamma)modules of padic Hodge theory. We will describe new proofs of
some results on finiteness of cohomology of these modules, and indicate
their applications to the theory of $p$adic families of automorphic
forms. This is part of ongoing work with Eugen Hellmann and Ruochuan Liu.


5:00pm 


6:00pm 

