Fri, October 25, 2019
Public Access Category: All |
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- Time:
- 2:30pm-3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- 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 Raghunathan’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.
- Time:
- 4:00pm-5:00pm
- Location:
- Room No. 215 Department of Mathematics
- 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 pseudo-deformation rings.
Abstract: Given a prime p, an integer N and a 2 dimensional
pseudo-representation of G_{Q,Np} over a finite field of characteristic p,
we will analyze how the structure of the universal pseudo-deformation 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
pseudo-representation arises from an actual representation. The talk will
begin with a brief survey of the theory of pseudo-representations.
- Time:
- 4:00pm-5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- 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.