8:00am 


9:00am 


10:00am 


11:00am 


12:00pm 


1:00pm 


2:00pm 
[2:30pm] Prasuna Bandi:TIFR Mumbai
 Description:
 Number theory seminar II.
Speaker: Prasuna Bandi.
Affiliation: TIFR Mumbai.
Date and Time: Friday 25 October, 2:30 pm  3:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Simultaneous density of integer values for an inhomogeneous
quadratic form and a linear form.
Abstract: In 1929 Oppenheim conjectured that for a nondegenerate,
indefinite, irrational quadratic form Q in n ≥ 5 variables, Q(Zn) is
dense in R. It was later strengthened to n ≥ 3 by Davenport and
proved in 1987 by Margulis based on Raghunathanâ€™s conjecture on closures
of unipotent orbits.
Later, Dani and Margulis proved the simultaneous density at integer values
for a pair of quadratic and linear form in 3 variables when certain
conditions are satisfied. We prove an analogue of this for the case of an
inhomogeneous quadratic form and a linear form.


3:00pm 

4:00pm 
[4:00pm] Shaunak Deo:TIFR Mumbai
 Description:
 Number theory seminar III.
Speaker: Shaunak Deo.
Affiliation: TIFR Mumbai.
Date and Time: Friday 25 October, 4:00 pm  5:00 pm.
Venue: Room 215, Department of Mathematics.
Title: Effect of level raising on pseudodeformation rings.
Abstract: Given a prime p, an integer N and a 2 dimensional
pseudorepresentation of G_{Q,Np} over a finite field of characteristic p,
we will analyze how the structure of the universal pseudodeformation ring
changes after allowing ramification at a prime $\ell$ not dividing Np.
This question has been studied by Boston and Bockle for deformation rings
of absolutely irreducible representations and Borel representations,
respectively. As a related question, we will also determine when a
pseudorepresentation arises from an actual representation. The talk will
begin with a brief survey of the theory of pseudorepresentations.
[4:00pm] Tathagata Basak : Iowa State University Mathematics Colloquium
 Description:
 Mathematics Colloquium II.
Speaker: Tathagata Basak.
Affiliation: Iowa State University.
Date and Time: Friday 25 October, 4:00 pm  5:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: A couple of curious reflection groups.
Abstract: Reflection groups occur all over representation theory and
geometry. We want to begin with a quick survey of finite reflection
groups, talk a little about classifying them and their connections to some
other areas of mathematics.
Then we want to focus on two examples of hyperbolic reflection groups; one
real and one complex. Both examples involve the Leech lattice; the lattice
that produces the best packing of spheres in 24 dimensional Euclidean
space. Both examples are (probably) related to the largest sporadic finite
simple group known as the monster. The connection in the complex case is
still a conjecture.
We will not assume any previous familiarity with hyperbolic reflection
groups or the Leech lattice or the Monster.


5:00pm 


6:00pm 

