Date and Time: Monday 23 September, 3:30 pm - 5:00 pm.
Venue: Room 215, Department of Mathematics.
Title: Paul Robert's Theorem.
Abstract: Let a finite abelian group G act on a normal local domain R
with residue field of R of char. 0. Assume that R^G is a UFD. Then R is a
free R^G- module. In particular, if R^G is regular then R is Cohen
Macaulay.
We will start preparation for P. Samuel's descent theory.
Time:
4:00pm-5:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Mathematics Colloquium Talk I.
Speaker: Agnid Banerjee.
Affiliation: TIFR-CAM, Bangalore.
Date and Time: Monday 23 September, 4:00 pm - 5:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: The structure of the regular and the singular set of the free
boundary in the obstacle problem for fractional heat equation.
Abstract: In this talk, I will discuss the structure of the free boundary
in the obstacle problem for fractional powers of the heat operator. Our
results are derived from the study of a lower dimensional obstacle problem
for a class of local, but degenerate, parabolic equations. The analysis
will be based on new Almgren, Weiss and Monneau type monotonicity formulas
and the associated blow-up analysis. This is a joint work with D.
Danielli, N. Garofalo and A. Petrosyan.
Time:
2:45pm-3:45pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Mathematics Colloquium Talk II.
Speaker: Amalendu Krishna.
Affiliation: TIFR, Mumbai.
Date and Time: Wednesday 25 September, 2:45 pm - 3:45 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Revisiting Bertini theorems.
Abstract: The classical Bertini theorem in algebraic geometry says that a
general hyperplane section of a smooth quasi-projective subvariety of a
projective space over an algebraically closed field is also smooth. It was
already known long time ago that such a result holds over any infinite
field. However, this turned out to be false over finite field, as Katz
showed. Poonen then showed that Bertini theorem can be salvaged over
finite fields by allowing hypersurfaces of large degree rather than just
hyperplanes. In this talk, we shall revisit these Bertini theorems. In
particular, we shall prove new Bertini theorems for normal and integral
schemes over finite fields. This is based on a joint work with Mainak
Ghosh.
Time:
4:00pm-5:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Mathematics Colloquium Talk III.
Speaker: Omprokash Das.
Affiliation: TIFR, Mumbai.
Date and Time: Wednesday 25 September, 4:00 pm - 5:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Birational classification of algebraic varieties.
Abstract: Algebraic varieties are common solutions of bunch of
multi-variable polynomials equations, for example, straight line, circle,
cuspidal curve, nodal curve, sphere, etc. Classifying all algebraic
varieties up to isomorphism is the ultimate goal of algebraic geometry. Of
course, this is nearly impossible achieve, so we consider various weaker
form of classification, and classifying varieties ‘Birationally’ is of
those tools. In this talk I will explain what it means to classify
varieties birationally, what are the difficulties in higher dimensions and
the role of Minimal Model Program (MMP) in birational classification.
Time:
4:00pm-5:30pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
CACAAG seminar.
Speaker: Maria Mathew.
Affiliation: IIT Bombay.
Date and Time: Friday 27 September, 4:00 pm - 5:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Gubeladze's geometric proof of Anderson's conjecture, Lecture III.
Abstract: Let M be a finitely generated seminormal submonoid of the free
monoid \mathbb Z_+^n and let k be a field. Then Anderson conjectured that
all finitely generated projective modules over the monoid algebra k[M]
is free. He proved this in case n=2. Gubeladze proved this for all n using
the geometry of polytopes. In a series of 3 lectures, we will outline a
proof of this theorem.
Time:
5:30pm-6:30pm
Location:
Room No. 215 Department of Mathematics
Description:
Algebraic Groups seminar.
Speaker: Anupam Kumar Singh.
Affiliation: IISER Pune.
Date and Time: Friday 27 September, 5:30 pm - 6:30 pm.
Venue: Room 215, Department of Mathematics.
Title: z-classes in algebraic groups.
Abstract: Two elements of a group G are said to be z-equivalent if their
centralizers are conjugate within G. The z-equivalence is a weaker
relation than the conjugacy relation. Let G be an algebraic group defined
over a field k. Steinberg, proved that when G is a reductive group and k
is an algebraically closed field, G(k) has finitely many z-classes. This
result is generalised to more general base field k which are of type (F).
In this talk, we discuss the results on this problem.