Pre-synopsis Seminar

 Monday, 19 Feb, 9.45 am

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Venue: Ramanujan Hall

Host: Sudarshan Gurjar

Speaker: Priyanka Magar

Affiliation: IIT Bombay

Title: Smooth structures on PL-manifolds of dimensions between 8 and 10

Annual Progress Seminar

Monday, 19 Feb. 11 am

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Venue: Ramanujan Hall

Host: Tony Puthenpurakal

Speaker: Samarendra Sahoo

Affiliation: IIT Bombay

Title: Quasi-pure resolutions and some lower bounds of Hilbert coefficients of Cohen-Macaulay modules.

Pre-synopsis Seminar

 Monday, February 19, 2024, 4 PM

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 Venue: Ramanujan Hall, Department of Mathematics

 Host: Dipendra Prasad

 Speaker: Dibyendu Biswas

 Affiliation: IIT Bombay

 Title: Stability of Tensor Products and Branching Laws for Classical Groups

Abstract: We consider the decomposition of tensor products of an irreducible representation of GL(n, C) and of the corresponding representations of GL(n + 1, C) and prove a 'stability result' about such tensor products. We go on to discuss similar questions for classical groups. Then we also discuss the branching laws for the classical pairs (GL(m,C), GL(n, C)), (Sp(2m, C), Sp(2n, C)), (SO(q, C), SO(p, C)) for all m<n, and all q<p.

Algebraic Stacks lecture series

Tuesday, 20 February, 11:30 AM

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Venue: Room 113

Host: Sudarshan Gurjar

Speaker: Nitin Nitsure

Affiliation: Bhaskaracharya Pratishthana

Title: Separated and proper morphisms for algebraic stacks

Abstract: This talk is devoted to the generalization of algebraic stacks of the theory of separated and proper morphisms for schemes. We will begin by recalling the relevant basics of algebraic spaces and of algebraic stacks, and their morphisms, illustrated with elementary examples. This will be followed by a description of specializations of points on algebraic stacks, which is the background needed for the valuative criteria for universal closedness and separateness.

Lecture series on Bayesian analytics

20 and 22 Feb 11:35 am to 1:00 pm

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Venues: 

Ramanujan  Hall on 22nd Feb.

Room 216 on 20 Feb.

Host: Radhendushka Srivastava

Speaker: Prof. Sujit Ghosh, NCSU.

Title: A short course on "Bayesian Analytics in Practice".

Abstract: The Bayesian paradigm provides a natural and practical way for building complex analytical models by expressing the joint model through a sequence of simpler conditional models, making it useful for various hierarchical data structures. This series of lectures will first introduce the general notions of Bayesian methods via hierarchical models, and then expand the topic with the more realistic and complex models that have recently emerged as a result of current Machine Learning (ML) literature. These models will be illustrated through practical applications to various real case studies avoiding much of the theoretical underpinnings. However, pointers to relevant theory will be provided as supplements with additional resources. Participants with basic knowledge of probability theory and statistical inferential framework will find the lectures useful in expanding their toolkit with the advanced use of Bayesian analytical methods. Popular topics such as prior sensitivity analysis, model comparisons, and uncertainty quantification for machine learning methods will be covered. In particular, the lectures will provide the necessary theory and practice for handling missing and censored data, a topic largely ignored in traditional ML methods. The concepts and methods discussed will be demonstrated primarily using R software illustrations, but the methodologies presented can also be carried out by other software (e.g., Python). Group activities during lab will be encouraged, allowing participants to have a hands-on experience. 

Topology and Related Topics Seminar

Tuesday, 20 February 2024, 12:00-1:00

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Venue: Ramanujan Hall (Hybrid Lecture) (Speaker will be online). 

Host: Rekha Santhanam

Speaker: Suraj Krishna

Affiliation: Technion - Israel Institute of Technology

Title: Cubulating hyperbolic mapping tori.

Abstract: A group is cubulated if it acts properly and cocompactly on a CAT(0) cube complex, which is a generalisation of a product of trees. Cubulated groups possess remarkable algebraic and geometric features and are an important topic of study in geometric group theory. In this talk, I will show that semidirect products of hyperbolic groups with $\mathbb{Z}$, which are themselves hyperbolic, are cubulated. 

Two prominent examples of our setup are: (1) Mapping tori of fundamental groups of closed hyperbolic surfaces over pseudo-Anosov automorphisms, and (2) Mapping tori of free groups over atoroidal automorphisms.

Both of these classes of groups are known to be cubulated due to outstanding works. Our proof builds upon these two noteworthy results and places them in a unified framework. This is based on joint work with François Dahmani and Jean Pierre Mutanguha.

Algebraic Groups Seminar

Tuesday, February 20, 4 pm

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Venue: Ramanujan Hall

Host: Shripad M. Garge

Speaker: Shripad M. Garge

Affiliation: IIT Bombay, Mumbai

Title: Homogeneous Spaces - II

Abstract: We study homogeneous spaces for linear algebraic groups.

Commutative Algebra Seminar

Tuesday, 20 Feb, 4 pm—5 pm

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Venue: Room 215

Host: Tony J. Puthenpurakal

Speaker: Sudeshna Roy

Affiliation: TIFR Bombay

Title: Epsilon multiplicity in two-dimensional standard graded algebras

Abstract: The notion of epsilon multiplicity, a generalization of the Hilbert-Samuel multiplicity, was introduced by B. Ulrich and J. Validashti to detect the integral dependence of arbitrary ideals. This invariant is difficult to handle as there are examples where it can be irrational and the epsilon function is very far from being polynomial-like. Let $A$ be a standard graded normal domain of dimension two over a field with the unique homogeneous maximal ideal $m$. Let $I$ be a homogeneous ideal in $A$. Our objective is to show that the epsilon multiplicity of $I$ is a rational number.

Lecture series on Bayesian analytics

22 Feb 11:35 am to 1:00 pm

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Venues:  Ramanujan  Hall 

Host: Radhendushka Srivastava

Speaker: Prof. Sujit Ghosh, NCSU.

Title: A short course on "Bayesian Analytics in Practice".

Abstract: The Bayesian paradigm provides a natural and practical way for building complex analytical models by expressing the joint model through a sequence of simpler conditional models, making it useful for various hierarchical data structures. This series of lectures will first introduce the general notions of Bayesian methods via hierarchical models, and then expand the topic with the more realistic and complex models that have recently emerged as a result of current Machine Learning (ML) literature. These models will be illustrated through practical applications to various real case studies avoiding much of the theoretical underpinnings. However, pointers to relevant theory will be provided as supplements with additional resources. Participants with basic knowledge of probability theory and statistical inferential framework will find the lectures useful in expanding their toolkit with the advanced use of Bayesian analytical methods. Popular topics such as prior sensitivity analysis, model comparisons, and uncertainty quantification for machine learning methods will be covered. In particular, the lectures will provide the necessary theory and practice for handling missing and censored data, a topic largely ignored in traditional ML methods. The concepts and methods discussed will be demonstrated primarily using R software illustrations, but the methodologies presented can also be carried out by other software (e.g., Python). Group activities during lab will be encouraged, allowing participants to have a hands-on experience. 

Algebra and Number Theory Seminar

Thursday, 22 February 2024, 4:00 pm

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Venue: Ramanujan hall

Host: Sandip Singh

Speaker: Sumit Chandra Mishra

Affiliation: IISER Mohali

Title: Local-global principles for norms and products of norms over semi-global fields

Abstract: A well-known result of Hasse states that the local-global principle holds for norms over number fields for cyclic extensions. In other words, if L/F is a cyclic extension of number fields then an element \lambda \in F^{\times} is in the image of norm map N_{L/F}: L^{\times} \rightarrow F^{\times} if and only if \lambda is in the image of the norm map locally everywhere,  i.e., for  completions associated to all archimedean and non-archimedean places of F.  In this talk, we would discuss local-global principles for norms and product of norms over fields which are function fields of curves over complete discretely valued fields, for example, \mathbb{C}((t))(x).

Annual Progress seminar 

Friday, 23 February, 11:30 am -12:30 pm 

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Venue: Ramanujan Hall

Host: Rekha Santhanam 

Speaker: Lekha Das (22D0790)

Title: Whitehead's Theorem

Abstract: We aim to show that if f is a continuous mapping between CW complexes X and Y inducing isomorphisms on all homotopy groups, then f is a homotopy equivalence.