This is a 3-day meeting of mathematics research scholars interested in geometry and topology. The goal of this event is to encourage emerging geometers and topologists to share and exchange active research ideas in their fields. In addition to participants' talks there will be three mini-courses. The venue for the meeting is Chennai Mathematical Institute.

The registration closes May 15th.

The purpose of this meeting is to bring together graduate students in topology and give them the opportunity to give talks, expose them to new topics, and get to know other graduate students in their field. The schedule will consist of three mini-courses and talks given by students. Participants are invited to give talks, 30 minutes long, about topics they have been studying. The subject need not be original research, but simply something the speaker enjoys and wishes to share. Talks should, in particular, be accessible to an audience of graduate students of varying levels.

If you are interested in giving a talk then do register as soon as possible. As of now we have around 15 spots available; depending on the number of requests and the subject areas the organizers will finalize speakers by early June. The selected participants can send their title and abstract after the confirmation.

**Introduction to contact and symplectic topology **

Speaker: Dheeraj Kulkarni (IISER, Bhopal)

Abstract: The study of symplectic and contact structures has
grown in into a well-established area by itself. We plan to
give a brief survey of some important milestones in the
development of this field in the last 50 years. However, the
main of this mini-course is to explain how symplectic and
contact structures arise naturally in many contexts. We will
also discuss topological properties of these structures.
Finally, we will also present the current state of the art.

** Topology of toric manifolds **

Speaker: V. Uma (IIT M)

Abstract: We shall introduce quasitoric manifolds and small covers defined by Davis and Januszkiewicz and describe their topological
invariants like cohomology ring , fundamental group and the topological $K$-ring.

** LS-category and the topology of motion planning **

Speaker: Tulsi Srinivasan (Ashoka University)

Abstract: This mini course will introduce the Lusternik-Schnirelmann category and the related notion of topological complexity.
We will look at the history of the LS-category, the reason it continued to be of mathematical interest, and its current applications
to motion planning.

With this background in place, we define the

Abstract: Topology deals with study of structures. The basic notions of topology viz open, closed, frontier, connectedness, boundary, connectivity are closely associated to the field of Image Analysis. Rosenfeld introduced the notion of Digital Topology and he represented a digital image as a neighborhood graph and defined the topological notions by introducing the adjacency relation using the notions of connectivity (4- , 8-) between the pixels of the images. Though these representations are very much useful for the image analysis. But it contains connectivity and boundary paradoxes. To overcome these paradoxes, Kovalevsky developed a consistent topology namely of Abstract Cellular Complex (ACC) by introducing the notions of lower dimensional cells in an image. Further he established that every finite topological space with the T0-Separation property is isomorphic to Abstract Cellular Complex. Using the notions of ACC he proposed a boundary tracing algorithm for images which overcomes the paradoxes. Vijaya and Sai Sundara Krishnan implemented the Kovalevsky’s Boundary tracing algorithm for tracing a boundary of a digital images and compared with already existing algorithm. Our aim is to enhance the study of image analysis in ACC through lower dimensional cells.

In this talk, we generalize the above result to a simplicial complex \(X\) whose \(k\)-skeleton is a clique complex and to a simplicial complex which is a subcomplex of a clique complex having the same \(1\)-skeletons. As an application we show that the cohomology of Neighborhood complexes of a random graphs \(G(n, p)\) vanishes for certain range of probability \(p\). This is joint work with D. Yogeshwaran

- Adittya Chaudhuri (IISER Thiruvananthpuram)
- Amit Kumar Paul (IIT Kanpur)
- Aparajita (ISI)
- Arijit Nath (IIT Madras)
- Aritra Bhowmick (ISI)
- Chandan Singh (Delhi University)
- Debayan Goswami (University of Allahabad)
- Deepti Singh (IIT Kanpur)
- Dinesh Nayak (Central University of Rajasthan)
- Dipali Swain (Central University of Jharkhand)
- Ganesh Satpute (IISER Mohali)
- Gayatri Limaye (IISER Bhopal)
- K. Nivetha (Thiruvallur University)
- Mohammad Aamir Qayyoom (Integral University of Lucknow)
- Prerak Deep (IISER Bhopal)
- Priya Garg (IIT Bombay)
- Priya Sharma (Dayalbag Educational Institute)
- Ramandeep Singh Arora (IISER Mohali)
- Ramya Nair (IISER Pune)
- Neha Nanda (IISER Mohali)
- Rishabh Gupta (IIT Kanpur)
- Sagar Shinde (IISER Bhopal)
- Sambit Senapati (CMI)
- Sayantan Goswami (BHU)
- Shilpa saini (IISER Bhopal)
- Shreya Banerjee (IISER Kolkata)
- Soumyajit Saha (IIT Bhopal)
- Sourayan Banerjee (IISER Bhopal)
- Sunanda Sinha (University of Calcutta)
- Vidit Das (IISER Bhopal)

- All the participants will be provided accommodation at the CMI hostel from the evening of July 15th till the afternoon of July 19th.
- Breakfast, meals, tea-coffee and snacks will be provided.
- Unfortunately we have very limited funding and hence are unable to provide travel support to all the participants. We request participants to use their contingency. However, feel free to get in touch with the organizers in case of any difficulty.

Address

Chennai Mathematical Institute

H1, SIPCOT IT Park

Siruseri, Tamil Nadu, 603 103

Click here
for directions.

+91-44-2747
0226 to 0229