Lecture 1 (by Dr. Gianluca Faraco, May 09, Saturday, 5 PM Indian time):

Title: Generating the mapping class group (Notes)

Lecture 2 (by Dr. Gianluca Faraco, May 14, Thursday, 5 PM Indian time):

Title: The Torelli subgroup of the mapping class group (Notes)

Lecture 3 (by Dr. Gianluca Faraco, May 20, Wednesday, 5 PM Indian time):

Title: The Baer-Dehn-Nielsen theorem (Notes)

Lecture 4 (by Dr. Soumya Dey, May 27, Wednesday, 5 PM Indian time):

Title: Geodesic laminations, train tracks : an intro

Lecture 5 (by Dr. Soumya Dey, May 30, Saturday, 5 PM Indian time):

Title: Measured foliations, Penner's construction of pseudo Anosovs

Lecture 6 (by Dr. Krishnendu Gongopadhyay, June 06, Saturday, 5 PM Indian time):

Title: Geometric structures on manifolds

Lecture 7 (by Dr. Gianluca Faraco, June 13, Saturday, 6 PM Indian time):

Title: Teichmüller spaces from different points of view and the relations among them

Lecture 8 (by Dr. Gianluca Faraco, June 17, Wednesday, 5 PM Indian time):

Title: Metric geometry of Teichmüller space

Lecture 9 (by Dr. Chris Leininger, June 20, Saturday, 8 PM Indian time):

Title: Mapping tori of pseudo-Anosovs

Abstract: In this talk I will discuss the geometry, topology, and dynamics of pseudo-Anosov mapping tori, following work of Thurston, Fried, McMullen, and others. The topics will include hyperbolization, the Thurston norm, and sections of pseudo-Anosov flows.

Lecture 10 (by Dr. Chris Leininger, June 22, Monday, 8 PM Indian time):

Title: Convex cocompact subgroups of the mapping class group

Abstract: In this talk, I will describe a coarse generalization of Thurston's hyperbolization for mapping tori that applies to extension groups. The topics will include the geometry of Teichmüller space, the curve complex, and actions of subgroups of the mapping class group on these.

Lecture 11 (by Dr. François Guéritaud, June 30, Tuesday, 5 PM Indian time):

Title: Veering triangulation

Lecture 12 (by Dr. Mahan Mj, July 11, Saturday, 5 PM Indian time):

Title: Percolation on hyperbolic groups

Abstract: We study first passage percolation (FPP) in a Gromov-hyperbolic group G with boundary equipped with the Patterson-Sullivan measure. We associate an i.i.d. collection of random passage times to each edge of a Cayley graph of G, and investigate classical questions about asymptotics of first passage time as well as the geometry of geodesics in the FPP metric. Under suitable conditions on the passage time distribution, we show that the 'velocity' exists in almost every direction, and is almost surely constant by ergodicity of the G-action on the boundary. For every point on the boundary, we also show almost sure coalescence of any two geodesic rays directed towards the point. Finally, we show that the variance of the first passage time grows linearly with word distance along word geodesic rays in every fixed boundary direction. This is joint work with Riddhipratim Basu.

Lecture 13 (by Dr. François Guéritaud, July 14, Tuesday, 5 PM Indian time):

Title: Uniform Lipschitz extension in bounded curvature

Lecture 14 (by Dr. Arpan Kabiraj, August 01, Saturday, 5 PM Indian time):

Title: Symplectic geometry of Teichmüller space: introduction and motivation (Part 1)

Lecture 15 (by Dr. Alex Casella, August 04, Tuesday, 5:30 PM Indian time):

Title: Moduli spaces of real projective structures: lecture 1

Outline: Start with an overview on the lecture series. Introduction to projective geometry and projective structures on surfaces. Then moduli spaces of properly convex structures.

Lecture 16 (by Dr. Arpan Kabiraj, August 08, Saturday, 5 PM Indian time):

Title: Symplectic geometry of Teichmüller space: introduction and motivation (Part 2)

Lecture 17 (by Dr. Alex Casella, August 11, Tuesday, 5:30 PM Indian time):

Title: Moduli spaces of real projective structures: lecture 2

Outline: Fock and Goncharov moduli space of framed projective structures, and their parametrisation

Lecture 18 (by Dr. Alex Casella, August 18, Tuesday, 5:30 PM Indian time):

Title: Moduli spaces of real projective structures: lecture 3

Outline: Properties and applications of FG parametrization

Lecture 19 (by Dr. Alex Casella, August 29, Saturday, 5:30 PM Indian time):

Title: Moduli spaces of real projective structures: lecture 4

Outline: Coordinates in dimension 3

Lecture 20 (by Dr. Kashyap Rajeevsarathy, September 19, Saturday, 5:00 PM Indian time):

Title: Geometric realizations of cyclic actions on surfaces : lecture 1 (notes)

Abstract: available here

Lecture 21 (by Dr. Kashyap Rajeevsarathy, September 26, Saturday, 5:00 PM Indian time):

Title: Geometric realizations of cyclic actions on surfaces : lecture 2

Lecture 22 (by Dr. Kashyap Rajeevsarathy, October 03, Saturday, 5:00 PM Indian time):

Title: Geometric realizations of cyclic actions on surfaces : lecture 3

Lecture 23 (by Neeraj K. Dhanwani, October 17, Saturday, 5:00 PM Indian time):

Title: Writing periodic maps as words in Dehn twists : lecture 1

Abstract: In this talk, we will discuss a procedure for expressing a finite order mapping class as a product of Dehn twists, up to conjugacy. This algorithm is based on the chain and star and generalized star relations in the mapping class group, the geometric realizations of torsion elements, and the symplectic representations of finite order mapping classes. As an application, we use this algorithm to write the roots of Dehn twists as words in Dehn twists.

Lecture 24 (by Neeraj K. Dhanwani, October 20, Tuesday, 5:00 PM Indian time):

Title: Writing periodic maps as words in Dehn twists : lecture 2

Lecture 25 (by Dr. Kuldeep Saha, October 27, Tuesday, 5:00 PM Indian time):

Title: Smooth embedding of 3 and 4 manifolds via open books and Lefschetz fibrations : lecture 1

Abstract: Study of smooth embedding of manifolds in simple spaces is one of the oldest and fundamental tool to understand the topology of manifolds. In recent times, some more hands on techniques have been used to show embedding results for smooth manifolds. The main ingredients used in this approach are open book decompositions and Lefschetz fibrations. We will discuss these developments in detail and try to formulate some open problems.

Lecture 26 (by Dr. Kuldeep Saha, October 31, Saturday, 5:00 PM Indian time):

Title: Smooth embedding of 3 and 4 manifolds via open books and Lefschetz fibrations : lecture 2

Lecture 27 (by Dr. Atreyee Bhattacharya, November 07, Saturday, 4:30 PM Indian time):

Title: On a certain rigidity of quasi Einstein metrics : lecture 1

Abstract: available here

Lecture 28 (by Dr. Atreyee Bhattacharya, November 13, Friday, 4:30 PM Indian time):

Title: On a certain rigidity of quasi Einstein metrics: lecture 2

Lecture 29 (by Chaitanya Tappu, November 18, Wednesday, 6:30 PM Indian time):

Title: Classification of infinite type surfaces

Abstract: In this talk I will sketch a proof of the classification theorem for surfaces (possibly noncompact or infinite type). Connected orientable surfaces are classified by their genus, space of ends, and its subspace spanned by genus. I will also briefly mention the modifications to the theorem dropping the orientability hypothesis, and the case of bordered surfaces.

Lecture 30 (by Dr. Kathryn Mann, November 21, Saturday, 6:30 PM Indian time):

Title: Big mapping class groups and their geometry : lecture 1

Abstract: I will give an introduction to mapping class groups of infinite type surfaces, and some of their algebraic and topological properties. In the second lecture, I will describe how to do geometric group theory with these groups (and other groups that are not finitely generated) and explain some ideas from recent joint work with Kasra Rafi.

Lecture 31 (by Dr. Kathryn Mann, November 28, Saturday, 6:30 PM Indian time):

Title: Big mapping class groups and their geometry : lecture 2

Lecture 32 (by Sandipan Dutta, December 05, Saturday, 5:00 PM Indian time):

Title: Geometric invariants under the Möbius action of SL(2,R)

Abstract: In this talk, we have considered all the possible continuous subgroups of the Lie group SL(2, R) (upto conjugacy) from dimension zero to three. For each of the classification, we have defined group action on the same line as Kisil. Möbius transformation have been taken as the corresponding action. This action is defined on the homogeneous spaces of various dimensions generated by the subgroups.

We have also introduced new invariant geometric objects in the homogeneous spaces of complex, double and dual numbers for the principal group SL(2,R), in the Kleins Erlangen Program. We have considered the action as the Möbius action and have taken the spaces as the spaces of complex, dual and double numbers. Some new decompositions of SL(2,R) have been used.

Lecture 33 (by Dr. Sushil Bhunia, December 12, Saturday, 5:00 PM Indian time):

Title : Twisted conjugacy in big mapping class groups

Abstract: Let φ be an automorphism of a group G. Two elements x and y of G are said to be φ-twisted conjugate if gx =yφ(g) for some g in G. This is an equivalence relation on G, and the equivalence classes are called the φ-twisted conjugacy classes or the Reidemeister classes of φ. If φ = Id, then the φ-twisted conjugacy classes are the usual conjugacy classes. A group G is said to have the R_{∞} -property if the number of its φ-twisted conjugacy classes is infinite for every automorphism φ of G. In this talk I will describe when a big mapping class group (i.e., mapping class group of an infinite type surface) possesses the R_{∞} -property. This is a work in progress with Swathi Krishna.