- Time:
- 4:00pm
- Location:
- Room No 114, Department of Mathematics
- Description:
Algebraic Groups seminar

Tuesday, 1 August 2023, 4 pm

=====================

Venue: Room 114

Host: Shripad Garge

Speaker: Dibyendu Biswas

Affiliation: IIT Bombay

Title: Commutative unipotent groups - II

Abstract: We continue our study of additive functions to understand commutative unipotent groups.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Mathematics Colloquium**Wednesday, 2 August at 4 pm

======================

**Host:**UK Anandavardhanan**Venue:**Ramanujan Hall**Speaker:**V Srinivas**Affiliation:**IIT Bombay**Title:**What is the Hodge Conjecture?**Abstract:**The Hodge Conjecture is one of the famous unsolved problems in algebraic geometry over the complex number field. This talk will give an accessible introduction to this problem, meant for the non-expert. In the end, I will briefly discuss some related work of mine with A. Rosenschon.

- Time:
- 2:30pm - 3:45pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Topology and Related Topics Seminar**Tuesday, 8 August 2023, 2.30 -3:45 pm

**=========================****Venue:**Ramanujan Hall**Host:**Rekha Santhanam**Speaker:**Priyanka Magar**Affiliation:**IIT Bombay**Title:**Essential Categorical Terms for Stable Homotopy Theory**Abstract:**In this talk, we will explore fundamental categorical terms necessary for understanding the stable homotopy theory. We'll begin by explaining the concept of a model category and its implications. Subsequently, we'll cover key terms like homotopy category and Quillen adjunction functors, etc

- Time:
- 3:30pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
Commutative Algebra Seminar

Tuesday, August 8, 2023, 3:30 pm

------------------------------------------

Venue: Room 215

Host: Tony Puthenpurakal

Speaker: Tony Puthenpurakal

Affiliation: IIT Bombay

Title: Triangulated and Derived Categories I

Abstract: We give an introduction to Triangulated categories.

- Time:
- 3:45pm
- Location:
- Room No. 113, Department of Mathematics
- Description:
**Seminar on Optimal Transport**Tuesday, 8 August 2023, 03.45 pm

=========================

**Venue:**Room 113, Department of Mathematics**Host:**Harsha Hutridurga**Speaker:**Saumyajit Das**Affiliation:**IIT Bombay**Title:**Introduction to Optimal Transport

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Algebraic Groups seminar Tuesday, 8 August 2023, 4 pm ====================== Venue: Ramanujan Hall Host: Shripad Garge Speaker: Chayan Karmakar Affiliation: IIT Bombay Title: Derivations and Tangent Spaces - I Abstract: We begin the study of derivations with the aim of introducing Lie algebras for algebraic groups.

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Lecture series in algebraic geometry Introduction to Hodge Theory --------------------------------------------- Wednesday, 9 August, 11.30--1.00 Thursday, 10 August, 11.30-1.00 ---------------------------------------------- Venue: Ramanujan Hall Host: Sudarshan Gurjar Abstract: This is the first lecture of a semester course of lectures on Hodge Theory

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Mathematics Colloquium Wednesday, 9 Aug. 2023, 4 pm ======================= Host: Sudarshan Gurjar Venue: Ramanujan Hall Speaker: Pallav Goyal Affiliation: University of Chicago Title: Almost commuting variety and quantum Hamiltonian reduction Abstract: I'll be talking about the notions of commuting varieties and almost commuting varieties of Lie algebras in Types A and C. Then I'll quantize these notions and discuss their applications to the representation theory of rational Cherednik algebras via Hamiltonian reduction.

- Time:
- 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**CACAAG Seminar**Wednesday, 9 August, 5.30 pm

-----------------------------------

**Venue:**Ramanujan Hall**Host:**Madhusudan Manjunath**Speaker:**Madhusudan Manjunath, IIT Bombay**Title:**The g-Conjecture for Simplicial Polytopes**Abstract:**We will sketch a proof of this conjecture and discuss some possible topics for further study

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Lecture series in algebraic geometry Introduction to Hodge Theory --------------------------------------------- Wednesday, 9 August, 11.30--1.00 Thursday, 10 August, 11.30-1.00 ---------------------------------------------- Venue: Ramanujan Hall Host: Sudarshan Gurjar Abstract: This is the first lecture of a semester course of lectures on Hodge Theory

- Time:
- 2:00pm - 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Lecture series in algebraic geometry Algebraic Stacks Thursday, 10 August, 2.30-4.00 pm --------------------------------------------- Venue : Ramanujan Hall Host: Sudarshan Gurjar Speaker: Nitin Nitsure, TIFR, Mumbai (retd) Abstract: I deliver a course of lectures on Algebraic Stacks .The tentative plan is to cover the first 100 pages or so of `Champs Algebriques' by Laumon and Moret-Bailly, which is the standard reference for the subject. Examples, definitions, and statements of results will be discussed in detail, and proofs of the main theorems will be sketched, focusing on the key ideas.

- Time:
- 2:30pm - 3:45pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
**Topology and Related Topics Seminar**Thursday, 10 August 2023, 2.30 -3:45 pm

==========================

**Venue:**Room 215**Host:**Rekha Santhanam**Speaker:**Sahin Mandal**Affiliation:**IIT Bombay**Title:**Vector Bundles and their Classification-1**Abstract:**In this talk, we define vector bundles and discuss some examples. We then talk about Stiefel and Grassmanian manifolds and explain how to construct new vector bundles from the old ones. Later we will talk about the classification of vector bundles in which will see how homotopy maps behave and construct the universal vector bundle.

- Time:
- 12:00pm - 1:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Ph. D. Defence seminar**Friday, 11 Aug,12:00 PM - 01:00 PM

**------------------------------------------**Sudarshan Gurjar

Host:**Venue:**Ramanujan Hall**Speaker:**Poonam Pokale, IIT Bombay**Title:**Topology of surfaces and Classification of affine curves

- Time:
- 3:45pm
- Location:
- Room No. 113, Department of Mathematics
- Description:
**Seminar on Optimal Transport**Friday, 11 August 2023, 03.45 pm

=========================

**Venue:**Room 113, Department of Mathematics**Host:**Harsha Hutridurga**Speaker:**Saumyajit Das**Affiliation:**IIT Bombay**Title:**Introduction to Optimal Transport

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Algebraic Geometry seminars****Lecture series on algebraic stacks**Monday, 14th August, 11:30 am

-------------------------------------------

**Venue:**Ramanujan Hall**Host:**Sudarshan Gurjar

**Speaker :**Nitin Nitsure

**Title:**Algebraic Stacks-I

**Abstract:**This will be the first lecture in a semester-long course on algebraic stacks.

- Time:
- 3:15pm - 4:15pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Ph. D. Defence seminar**Monday, 14 Aug, 3.15 pm-- 4.15 pm

**------------------------------------------****Host:**Shantanu Dey**Venue:**Ramanujan Hall**Speaker:**M. N. Reshami, IIT Bombay**Title:**Multi-Analytic Operators, Colligations, and Functional Models

- Time:
- 11:00am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Algebraic Geometry seminars****Lecture series on Hodge Theory**Wed. Thu., 16, 17 August, 11.00 am

-----------------------------------------

**Venue:**Ramanujan Hall**Host:**Sudarshan Gurjar**Title:**Introduction to Hodge Theory-3,4

**Speaker:**V. Srinivas, IIT Bombay

- Time:
- 11:00am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Algebraic Geometry seminars****Lecture series on Hodge Theory**Wed. Thu., 16, 17 August, 11.00 am

-----------------------------------------

**Venue:**Ramanujan Hall**Host:**Sudarshan Gurjar**Title:**Introduction to Hodge Theory-3,4

**Speaker:**V. Srinivas, IIT Bombay

- Time:
- 2:30pm - 3:45pm
- Location:
- Room No 215, Department of Mathematics
- Description:
Topology and Related Topics Seminar

Thursday, 17 August 2023, 2.30 -3:45 pm

===========================

Venue: Room 215

Host: Rekha Santhanam

Speaker: Sahin Mandal

Affiliation: IIT Bombay

Title: Vector Bundles and their Classification-2.

Abstract:

We will continue to talk about the classification of vector bundles in which will see how homotopy maps behave and construct the universal vector bundle. If time permits we will delve into topological K-theory.

- Time:
- 3:45pm
- Location:
- Room No. 113, Department of Mathematics
- Description:
**Seminar on Optimal Transport**Friday, 18 August 2023, 03.45 pm

======================

**Venue:**Room 113, Department of Mathematics**Host:**Harsha Hutridurga**Speaker:**Saumyajit Das**Affiliation:**IIT Bombay**Title:**Introduction to Optimal Transport

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Lecture series on algebraic stacks**Monday, 21 August, 11:30 am

----------------------------------------------

**Venue**: Ramanujan Hall**Host:**Sudarshan Gurjar

**Speaker :**Nitin Nitsure**Affiliation:**TIFR, Mumbai (retd)

**Title:**Algebraic Spaces**Abstract:**In his talk `The Implicit Function Theorem in Algebraic Geometry', delivered in the legendary conference `Algebraic Geometry, Bombay-1968', Michael Artin expanded the category of spaces used in algebraic geometry by introducing `algebraic spaces', which was a step beyond the schemes of Grothendieck. In the 55 years that have passed since then, algebraic spaces have become an important part of Algebraic Geometry. In particular, the theory of algebraic stacks makes foundational use of them.

In this lecture, we will introduce algebraic spaces, just assuming that the audience is familiar with schemes at the level of the first few sections of Chapter 2 of Hartshorne's textbook Algebraic Geometry'. After giving some motivation and examples, some basic properties of algebraic spaces will be outlined.

This lecture is the beginning of a series of about 12 talks titled `An introduction to Algebraic Stacks'. The aim of this series is to cover the first half of the textbook `Champs Algebriques' by Laumon and Moret-Bailly. This knowledge is essential in order to follow a whole lot of modern research in both arithmetic and geometry.

- Time:
- 2:15pm - 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Topology and Related Topics Seminar

Tuesday, 22 August 2023, 2.15 -3:30 pm

===========================

Venue: Ramanujan Hall, Department of Mathematics

Host: Rekha Santhanam

Speaker: Priyanka Magar

Affiliation: IIT Bombay

Title: A brief introduction to the stable homotopy category

Abstract:

The talk will begin with some stable phenomenon that guides us to the Spanier-Whitehead category, which has its own interesting properties. Next, we'll explore how the Brown representability theorem brings in the idea of Spectra and, as a consequence, gives rise to the stable homotopy category.

- Time:
- 3:30pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
**Commutative Algebra Seminar**Tuesday, August 22, 3:30 pm

---------------------------------------------

**Venue :**Room 215**Host:**Tony Puthenpurakal**Speaker:**Tony Puthenpurakal**Affiliation:**IIT Bombay**Title:**Triangulated and Derived Categories-2**Abstract:**We continue our introduction to Triangulated categories

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Algebraic Groups seminar**Tuesday, 22 August 2023, 4 pm

**====================****Venue:**Ramanujan Hall**Host:**Shripad Garge**Speaker:**Chayan Karmakar**Affiliation:**IIT Bombay**Title:**Derivations and Tangent Spaces - II

**Abstract:**We study derivations with the aim of introducing Lie algebras for algebraic groups.

- Time:
- 5:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Combinatorics, Commutative Algebra and Algebraic Geometry (CACAAG) Seminar**Wednesday, 23 August, 5:30 pm

========================================================

**Host:**Madhusudan Manjunath**Venue:**Ramanujan Hall.**Speaker:**Madhusudan Manjunath**Title:**The Chow Ring of a simplicial toric variety.**Abstract:**We will give a combinatorial presentation of the Chow ring of a simplicial toric variety and discuss its applications.

- Time:
- 10:00am - 11:00am
- Location:
- Room No 215, Department of Mathematics
- Description:
Annual progress seminar Date: 24th August, 2023 Time: 10:00 AM -- 11:00 AM Venue: Room 215 Host: Manoj Keshari Speaker: Sai Krishna Title: An algebraic characterization of the affine three space in arbitrary characteristic Abstract: We give an algebraic characterization of the affine three space over an algebraically closed field of arbitrary characteristic. We will look at a possible application of this characterization to reformulate the question of whether certain ring is isomorphic to the polynomial ring in three variables over an algebraically closed field of positive characteristic.

- Time:
- 2:00pm - 2:35pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Annual Progress Seminar Time: 02:00 PM -- 02:35 PM Host: Sourav Pal Speaker: Priyanka Aroda Title: Contractions and their dilations Abstract: A contraction is an operator on a Hilbert space which has norm atmost 1. We study Sz.-Nagy's dilation theorem which models contractions as a part of nicer operators on larger spaces. We also discuss a more direct and explicit construction of a unitary dilation of a contraction, which is due to Schaffer. We study an analogue to Sz.-Nagy's dilation theorem, due to Ando, for a pair of commuting contractions.

- Time:
- 2:30pm - 3:45pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
**Topology and Related Topics Seminar**Thursday, 24 August 2023, 2.30 -3:45 pm

=============================

**Venue:**Room 215**Host:****Speaker:**Soumya Deb Samanta**Affiliation:**IIT Bombay**Title:****Abstract:**In this talk, I will give a brief introduction to the different aspects of Riemannian geometry: Riemannian metrics, affine connections, covariant derivatives, geodesics, curvature, Jacobi fields, and variation formulas. This talk will serve as a prelude to my next talk which will involve some topological aspects of Riemannian Manifolds.

- Time:
- 2:40pm - 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Analysis Seminar Time: 02:40 PM -- 03:30 PM Host: Sourav Pal Speaker: Saikat Roy Title: Applications of Birkhoff-James orthogonality and its connection with dilation Abstract: Birkhoff-James orthogonality is a generalized notion of orthogonality that extends the inner product orthogonality to the setting of Banach spaces. In this talk, we present some of its applications in geometry of Banach spaces and its relation with norming properties of some subspaces of Banach space. We also consider operator orthogonality and its connection with the unitary and isometric dilations. We study the case when unitary (isometric) dilations of two contractions preserve the orthogonality relation between the basic contractions.

- Time:
- 11:30am - 1:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Lecture series on algebraic stacks**Monday, 28 August, 11:30 am-1.00 pm

----------------------------------------------

**Venue**: Ramanujan Hall**Host:**Sudarshan Gurjar

**Speaker :**Nitin Nitsure**Affiliation:**TIFR, Mumbai (retd)

**Title:**Algebraic spaces-II

**Abstract:**In his talk `The Implicit Function Theorem in Algebraic Geometry', delivered at the legendary conference `Algebraic Geometry, Bombay-1968', Michael Artin expanded the category of spaces used in algebraic geometry by introducing `algebraic spaces', which was a step beyond the schemes of Grothendieck. In the 55 years that have passed since then, algebraic spaces have become an important part of Algebraic Geometry. In particular, the theory of algebraic stacks makes foundational use of them.

In this lecture, we will introduce algebraic spaces, just assuming that the audience is familiar with schemes at the level of the first few sections of Chapter 2 of Hartshorne's textbook Algebraic Geometry'. After giving some motivation and examples, some basic properties of algebraic spaces will be outlined.

This lecture is the beginning of a series of about 12 talks titled `An Introduction to Algebraic Stacks'. The aim of this series is to cover the first half of the textbook `Champs Algebriques' by Laumon and Moret-Bailly. This knowledge is essential in order to follow a whole lot of modern research in both arithmetic and geometry.

- Time:
- 3:30pm - 4:30pm
- Location:
- Room No 215, Department of Mathematics
- Description:
**Commutative Algebra Seminar**Tuesday, August 29, 3:30 pm-4.30 pm

---------------------------------------------

**Venue:**Room 215**Host:**Tony Puthenpurakal**Speaker:**Tony Puthenpurakal, IIT Bombay**Title:**Triangulated and Derived Categories 3**Abstract:**We continue our introduction to Triangulated categories.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Algebraic Groups seminar**Tuesday, 29 August 2023, 4 pm

**====================****Venue:**Ramanujan Hall**Host:**Shripad Garge**Speaker:**Chayan Karmakar**Affiliation:**IIT Bombay**Title:**Derivations and Tangent Spaces - III

**Abstract:**We study derivations with the aim of introducing Lie algebras for algebraic groups.

- Time:
- 11:30am - 1:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Lecture series on Hodge Theory**Wednesday and Thursday

30 and 31 August, 11:30 am – 1.00 pm

**----------------------------------------------****Venue:**Ramanujan Hall**Host:**Sudarshan Gurjar

**Speaker:**V. Srinivas

**Affiliation:**IIT Bombay

**Title:**Introduction to Hodge Theory

**Abstract:**These are part of an ongoing series of lectures on the basics of Hodge theory. The next two lectures will finish the proof of the de Rham theorem, via sheaf cohomology, and if time permits, a beginning will be made on some linear algebra needed for the Hodge theory, as in Chapter 1 of Huybrechts' book.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Mathematics Colloquium**Wednesday, 30 August at 4.00-5.00 pm

====================

**Venue:**Ramanujan Hall**Host:**Saikat Mazumdar**Speaker:**Adimurthi, IIT Kanpur and TIFR-CAM, Bengaluru**Title:**Critical Fractional Laplacian

**Abstract:**Dyda obtained the embedding of the space of functions having finite Fractional Laplacian norm in his work. He has not covered the critical case and asked several questions. In this talk, I will explain his questions and how they can be handled. This is a joint work with Prosenjit, Purbita, and Vivek Sahu.

- Time:
- 5:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**CACAAG Seminar**Wednesday, 30 August, 5:30 PM

---------------------------------------

**Venue:**Ramanujan Hall.**Host:**Madhusudan Manjunath**Speaker:**Madhusudan Manjunath, IIT Bombay.**Title:**The Chow Ring of a Simplicial Toric Variety II.**Abstract:**We will continue our study of the Chow ring of a simplicial toric variety.

- Time:
- 11:30am - 1:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Lecture series on Hodge Theory**Wednesday and Thursday

30 and 31 August, 11:30 am – 1.00 pm

**----------------------------------------------****Venue:**Ramanujan Hall**Host:**Sudarshan Gurjar

**Speaker:**V. Srinivas

**Affiliation:**IIT Bombay

**Title:**Introduction to Hodge Theory

**Abstract:**These are part of an ongoing series of lectures on the basics of Hodge theory. The next two lectures will finish the proof of the de Rham theorem, via sheaf cohomology, and if time permits, a beginning will be made on some linear algebra needed for the Hodge theory, as in Chapter 1 of Huybrechts' book.

- Time:
- 2:30pm
- Location:
- Room No 215, Department of Mathematics
- Description:
**Topology and Related Topics**Thursday, 31 August 2023, 2.30 pm

======================

**Venue:**Room 215**Host:**Rekha Santhanam**Speaker:**Soumyadeb Samanta**Affiliation:**IIT Bombay**Title:**An Introduction to Riemannian Manifolds (contd.)

**Abstract:**This talk will be in continuation with the previous one. I plan to cover the following: geodesics, curvature, Jacobi fields, and variation formulas.