Dec'21 - June'22 Session
Organized by : Prerak Deep & Pooja Joshi
Embedded Files
Talk 20. [Dated 02.06.22]
A first Classification of Riemann Surfaces
A first Classification of Riemann Surfaces
by Rajesh Dey
Abstract
Riemann Surfaces are topological surfaces with an additional 'complex structure' which allows us to do complex analysis on them. Among them, simply connected Riemann surfaces are of special significance. The uniformization theorem tells us that there are only three such Riemann surfaces. As an application of this theorem and using basic tools from complex analysis and covering space theory, we will give a first classification of Riemann surfaces in this talk.Abstract
Talk 19. [Dated 19.05.22]
Ricci Curvature of Graphs
Ricci Curvature of Graphs
by Aditya TIwari
Abstract
The Ricci Curvature plays a crucial role in the analysis of manifolds. The Bonnet Myers theorems, Lichnerowicz theorem, and many other critical geometric results were obtained due to the bound on Ricci Curvature. The notion of the Ricci Curvature can be adopted to graphs along with some other geometric concepts, like the Differential operator, Laplace Operator, etc. In this talk, we will prove the Bonnet Myers type theorem and Lichnerowicz type theorem on Graphs.Abstract
Talk 18. [Dated 11.05.22]
Payne's Conjecture
Payne's Conjecture
by Aditya Tiwari
Abstract
Abstract
A conjecture of L. Payne states that for bounded domains in R2, the nodal line of any second eigenfunction of the Laplacian with zero boundary condition divides the domain by intersecting its boundary at exactly two points. In this talk, we will discuss this conjecture with the help of an example and talk about the cases proved until now.
Talk 17. [Dated 14.04.22]
Introduction to Teichmuller Spaces
Introduction to Teichmuller Spaces
by Satyajit Maity
Satyajit Maity is a second-year Ph.D. student in the Department of Mathematics, IISER Bhopal. He is currently working on mapping class group actions on Teichmuller spaces, under the supervision of Dr. Kashyap Rajeevsarathy and Dr. Atreyee Bhattacharya.by Satyajit Maity
Talk 16. [Dated 07.04.22]
Hurwitz groups and Hurwitz surfaces
Hurwitz groups and Hurwitz surfaces
by Rajesh Dey
Rajesh Dey is a 5th-year IPhd student in the Department of Mathematics at IISER Bhopal, India. He is currently working on "Mapping class group of surfaces," which is an active research topic in the area of low dimensional geometry and topology. He is doing his Ph.D. under the guidance of Dr. Kashyap Rajeevsarathy.by Rajesh Dey
Talk 15. [Dated 31.03.22]
Finite Group actions on Surfaces (Pt. 2)
Finite Group actions on Surfaces (Pt. 2)
by Rajesh Dey
Rajesh Dey is a 5th-year IPhd student in the Department of Mathematics at IISER Bhopal, India. He is currently working on "Mapping class group of surfaces," which is an active research topic in the area of low dimensional geometry and topology. He is doing his Ph.D. under the guidance of Dr. Kashyap Rajeevsarathy.by Rajesh Dey
Talk 14. [Dated 17.03.22]
Finite Group actions on Surfaces (Pt. 1)
Finite Group actions on Surfaces (Pt. 1)
by Rajesh Dey
Rajesh Dey is a 5th-year IPhd student in the Department of Mathematics at IISER Bhopal, India. He is currently working on "Mapping class group of surfaces," which is an active research topic in the area of low dimensional geometry and topology. He is doing his Ph.D. under the guidance of Dr. Kashyap Rajeevsarathy.by Rajesh Dey
Talk 13. [Dated 10.03.22]
Geometric Spaces
Geometric Spaces
by Shaivi Chavan
Shaivi Chavan is a fifth-year BS-MS student in the Department of Mathematics at IISER Bhopal, India. She is doing her master's thesis under the supervision of Dr. Atreyee Bhattacharya.by Shaivi Chavan
Seminar GT.pdfTalk 12. [Dated 03.03.22]
Lie Groupoids
Lie Groupoids
by Pooja Joshi
Pooja Joshi is a third-year integrated Ph.D. student in the department of Mathematics at IISER Bhopal, India. She is doing her thesis under the guidance of Dr. Atreyee Bhattacharya (IISER Bhopal) and Prof. Dr. Madeleine Jotz Lean (University of Wurzburg).by Pooja Joshi
GTS.pdfTalk 11. [Dated 23.02.22]
General Primitivity of Mapping Class group (Part 2)
General Primitivity of Mapping Class group (Part 2)
by Pankaj Kapdi
Mr. Pankaj Kapdi is a fourth-year Integrated Ph.D. student working on a Mapping class group of surfaces, under the supervision of Dr. Kashyap Rajeevsarathy.by Pankaj Kapdi
Talk 10. [Dated 17.02.22]
Twins and Doodles
Twins and Doodles
by Dr Neha Nanda
Dr. Neha Nanda is an Institute Postdoctoral Fellow in the Department of Mathematics, IISER Bhopal. She did her PhD from IISER Mohali, where she was also an Integrated-PhD candidate. Currently, she is working in the area of mapping class groups with Dr Kashyap Rajeevsarathy.by Dr Neha Nanda
Abstract:
In the broad area of knot theory, doodles serve as planar analogues of knots in Euclidean 3-space. These are related to groups called twin groups by the fundamental Alexander and Markov theorems. These objects can be defined in the higher genus setting with a more elaborate sense of equivalence, resulting in the theory of virtual doodles and virtual twins. In this talk, these notions will be discussed, concluding with the Alexander and Markov theorems for the virtual doodles. This work is in collaboration with Dr Mahender Singh.
Talk 9. [Dated 09.02.22]
Combination Problem in Geometric Group Theory
Combination Problem in Geometric Group Theory
by Dr. Suman Paul
Dr. Suman Paul is a Postdoctoral Fellow in our department. He did his PhD from IIT Kanpur. Currently, he is working in the field of Geometric group theory with Dr. Kashyap Rajeevsarathy.by Dr. Suman Paul
G_T_Seminar.pdfGTS.pdfTalk 8. [Dated 27.01.22]
General Primitivity of Mapping Class group
General Primitivity of Mapping Class group
by Pankaj Kapdi
Mr. Pankaj Kapdi is a fourth-year Integrated Ph.D. student working on a Mapping class group of surfaces, under the supervision of Dr. Kashyap Rajeevsarathy.by Pankaj Kapdi
Geometry and Topology Seminars (2022-01-20 at 03:35 GMT-8)Talk 7. [Dated 20.01.22]
What makes the Laplacian special?
What makes the Laplacian special?
by Aditya Tiwari
Aditya Tiwari is a 6th year Integrated PhD student in the department of Mathematics. He is working in Geometric Analysis under the supervision of Dr. Anandateertha Mangasuli.by Aditya Tiwari
Geometry and Topology Seminars (2022-01-13 at 04:36 GMT-8)Talk 6. [Dated 13.01.22]
Metacyclic Actions on Surfaces
Metacyclic Actions on Surfaces
by Apeksha Sanghi
Apeksha Sanghi is a sixth-year Ph.D. student in the department of Mathematics. She is working in the mapping class group under the supervision of Dr. Kashyap Rajeevsarathy.by Apeksha Sanghi
Geometry and Topology Seminars (2022-01-06 at 04:36 GMT-8)Talk 5. [Dated 06.01.22]
Contact Structure on $R^3$
Contact Structure on $R^3$
by Sannidhi A S
Sannidhi is a fourth year PhD student in the department of Mathematics at IISER Bhopal. Currently, he is working in the field of Contact Riemannian Geometry, under the supervision of Dr. Dheeraj Kulkarni and Dr. Atreyee Bhattacharya.by Sannidhi A S
Geometry and Topology Seminars (2021-12-30 at 04:35 GMT-8)Talk 4. [Dated 30.12.21]
Jones Polynomial and Khovanov Homology
Jones Polynomial and Khovanov Homology
by Monika
Monika is a fourth year PhD student in the department of Mathematics at IISER Bhopal. Monika did her MSc from IIT Kanpur. Currently, she is working in the field of Legendrian knot theory under the supervision of Dr. Dheeraj Kulkarni.by Monika
GaTs #3: Geodesic ray transform Shubham JatharTalk 3. [Dated 23.12.21]
Geodesics Ray Transform
Geodesics Ray Transform
by Shubham Jathar
Shubham Jathar is a fourth-year Int Ph.D. student at IISER Bhopal. He is working in Geometric Inverse Problems and Inverse problems related to Nonlinear PDEs under the supervision of Dr. Manas Kar. He completed his MS at IISER Bhopal. His MS thesis was on Inverse problems related to linear and nonlinear partial differential equations.by Shubham Jathar
cnz-jvmt-xbs (2021-12-18 at 03:40 GMT-8)Talk 2. [Dated 18.12.21]
Topological Surgery
Topological Surgery
by Prerak Deep
Prerak Deep is a third-year Ph.D. student. He is working in contact topology, particularly on a problem that involves 'Kirby's theorem' under the supervision of Dr. Dheeraj Kulkarni.[Email: prerakd@iiserb.ac.in]by Prerak Deep
Geometry and Topology Seminars (2021-12-09 at 04:37 GMT-8)Talk 1. [Dated 9.12.21]
Introduction to Mapping Class Groups.
Introduction to Mapping Class Groups.
by Harsh Patil
Harsh Patil is a first-year Ph.D. student at IISER Bhopal. He completed his BS-MS at IISER Bhopal. His MS thesis was on the topic 'Birman-Hilden Theory' which can broadly be described as the interaction between the theory of covering spaces and mapping class groups.by Harsh Patil
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