Date and Time: Monday 24 February, 03:30 pm - 05:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Cotangent complex and applications (A short series of lectures).
Abstract: Differential 1-forms are very useful in the study of
multivariate calculus or smooth manifolds. Algebraically, the module of
Kahler differentials is very useful in commutative algebra. When the
spaces (or varieties) are not smooth but have singularities, differential
1-forms are not enough. Instead there is available a more general gadget
called the cotangent complex in commutative algebra as well as in
algebraic geometry. This series of talks will begin by recalling usual
differential forms and Kahler differentials in familiar setting, and then
introduce the cotangent complex. Applications to smoothness, local
complete intersections and deformation theory will be shown. Some
familiarity with the language of commutative algebra will be assumed.
The first talk will be accessible to advanced undergraduate students.
Time:
4:00pm-5:00pm
Location:
Room No. G01, Computer Center (CC) Conference Room
Date and Time: Tuesday 25 February, 04:00 pm - 05:00 pm.
Venue: Room No. G01, Computer Center (CC) Conference Room.
Title: Non-uniqueness in law of stochastic 3D Navier-Stokes equations
Abstract: I will present a recent result obtained together with R. Zhu and
X. Zhu. We consider the stochastic Navier-Stokes equations in three
dimensions and prove that the law of analytically weak solutions is not
unique. In particular, we focus on two iconic examples of a stochastic
perturbation: either an additive or a linear multiplicative noise driven
by a Wiener process. In both cases, we develop a stochastic counterpart of
the convex integration method introduced recently by Buckmaster and Vicol.
This permits to construct probabilistically strong and analytically weak
solutions defined up to a suitable stopping time. In addition, these
solutions fail the corresponding energy inequality at a prescribed time
with a prescribed probability. Then we introduce a general probabilistic
construction used to extend the convex integration solutions beyond the
stopping time and in particular to the whole time interval [0,∞].
Finally, we show that their law is distinct from the law of solutions
obtained by Galerkin approximation. In particular, non-uniqueness in law
holds on an arbitrary time interval [0,T], T>0.
Time:
11:30am
Location:
Ramanujan Hall, Department of Mathematics
Description:
Statistics and Probability seminar.
Speaker: Nilanjan Chatterjee.
Affiliation: Johns Hopkins University.
Date and Time: Wednesday 26 February, 11:30 am - 12:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Statistical model building using data fusion.
Abstract: Many applications require development of complex statistical
models involving many variables. It may not, however, be possible to train
such model in a single dataset of adequately large sample size that has
measured all the variables. Instead, data may be available across multiple
studies, where any individual study may not measure all the variables, but
the different studies altogether cover all the variables. In this talk, I
will describe how to fit popular non-linear models, such as logistic
regression models, by combining information from such multiple disparate
data sources. In fact we will show it is possible to fit such models only
using "summary-level" information, i.e. estimates of parameters from
fitted simpler models, from individual studies and thus overcoming some
of the logistical and ethical issues related to sharing of individual
level data across studies. Methods will be illustrated through extensive
simulation studies and real data examples
Time:
2:30pm-3:30pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Geometry and Topology seminar.
Speaker: Arjun Paul.
Affiliation: IIT Bombay.
Date and Time: Wednesday 26 February, 02:30 pm - 03:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Fundamental group schemes of Hilbert scheme of n points on
irreducible smooth projective varieties of dimension 1 and 2.
Abstract: : Let k be an algebraically closed field of characteristic p > 3. Let X be an irreducible
smooth projective k-variety of dimension d ∈ {1, 2} over k. Fix an integer n ≥ 2, and let
Hilbn
X be the Hilbert scheme parametrizing effective 0-cycles of length n on X. In this talk
we discuss on the S-fundamental group scheme and Nori’s fundamental group scheme of
Hilbn
X. This is a joint work with Ronnie Sebastian.
Time:
4:00pm-5:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Mathematics Colloquium.
Speaker: Nilanjan Chatterjee.
Affiliation: Johns Hopkins University.
Date and Time: Wednesday 26 February, 04:00 pm - 05:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Disease risk prediction and causal inference using genome-wide
genetic data.
Abstract: Recent genome-wide association studies have led to
identification of thousands of genetic variants associated with complex
traits and diseases like adult height, body mass index, heart disease,
type-2 diabetes and cancer. The large scale genetic data, some of which
are publicly available, provide statisticians, mathematicians, computer
scientists and other quantitative researchers an incredible opportunity
for the development and applications of novel methods and algorithms. In
this talk, I will describe the work from our laboratory to harness the
power of these big datasets to address two most pressing problems in
public health research. In particular, I will describe simple and more
advanced machine learning methods for building genetic risk-scores from
these datasets that can be used to predict prospectively individuals' risk
of diseases. Further, I will describe how genetic data can be used to
conduct, "instrumental" variable analysis, an approach popular in
Economics, to understand causal relationship among risk-factors and health
outcomes.
Time:
4:30pm-5:30pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
CACAAG seminar.
Speaker: Madhusudan Manjunath.
Affiliation: IIT Bombay.
Date and Time: Thursday 27 February, 04:30 pm - 05:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Introduction to Tropical Algebraic Geometry, Part II: Applications.
Abstract: We will give a glimpse of applications of tropical geometry to
algebraic geometry, particularly the theory of algebraic curves. We will
also mention some potential topics for future work. The talk will not
assume any special background, PhD and MSc students are specially welcome.
Time:
4:00pm-5:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Algebraic Geometry seminar.
Speaker: Amit Tripathi.
Affiliation: IIT Hyderabad.
Date and Time: Friday 28 February, 04:00 pm - 05:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Vector bundles over complex projective hypersurfaces.
Abstract: In the first half of this talk I will discuss some results
related to existence (or rather non existence) of indecomposable low rank
vector bundles over complex projective space followed by similar questions
for hypersurfaces. The second half will be devoted to a generic version of
the BGS conjecture for ACM bundles on hypersurfaces and a recent joint
work with Girivaru Ravindra.