Mathematics Seminar Series 2020

Year   2020    2019    2018

Title:    Algorithms for Dynamical Systems

Speaker:    Dr. Nikhil Balaji, Research Associate, Computer Science, University of Oxford

Date:    July 07, 2020 (Tuesday)

Brief Bio:     Dr. Nikhil Balaji obtained his Ph.D. from the Chennai Mathematical Institue advised by Prof. Samir Datta. Subsequently, he has held postdoctoral positions at IIT Bombay, Ulm University, and the University of Oxford, where he is currently based. His research interests are broadly in theoretical computer science, and more specifically in automata theory, quantitative verification, and computational complexity.

Title:    Distal Actions of Automorphisms of Nilpotent groups G on SubG and applications to Lattices in Lie Groups.

Speaker:    Mr. Rajdip Palit, Jawaharlal Nehru University, Delhi

Date:    March 06, 2020 (Friday)

Brief Bio:     Rajdip Palit obtained an M.Sc. degree from Indian Institute of Technology (IIT), Madras in 2012. Currently, he is pursuing his Ph.D. in Mathematics from Jawaharlal Nehru University, Delhi. His area of interest is in Topology.

Title:    Proving Unsatisfiability of Constraint Satisfaction Problems

Speaker:    Prof. Daya Gaur, Department of Mathematics and Computer Science, University of Lethbridge

Date:    February 19, 2020 (Wednesday)

Abstract:     We describe a method to prove unsatisfiability of constraint satisfaction problems (CSP). The method relies on a structural decomposition of a CSP into constituent tensors. The decomposition is used to determine the unsatisfiability efficiently and in parallel. We give empirical evidence that the approach improves the praxis.

The talk will be self-contained and accessible to all students. Everyone is welcome.

Brief Bio:     Prof. Daya obtained a Bachelor of Technology (Hons) in Computer Science and Engineering from the Institute of Technology, Banaras Hindu University, Varanasi, and a Masters from Simon Fraser University. He got a PhD in Computer Science from Simon Fraser University. He is a Professor of Computer Science in the Department of Mathematics and Computer Science at the University of Lethbridge. His research interests are in Algorithms, Artificial Intelligence, Bioinformatics, and Quantum Technologies. He has held visiting appointments at TIFR Mumbai and Indian Institute of Technology (IIT) Delhi. He served as the founding Head, Department of Computer Science and Engineering, IIT Ropar, and as Head, Department of Mathematics, IIT Ropar.

Title:    What does a Mathematical Philosophy look like? : Notes from  Catastrophe TheoryAnalytics in Healthcare

Speaker:    Ravi Chakraborty, Department of Philosophy, IIT-Delhi

Date:    February 14, 2020 (Friday)

Abstract:     When one speaks of philosophy of mathematics, the concern is with the problem of the foundations of mathematics and not the specificity of actual mathematical techniques. However, the other perception of the exalted power of mathematics is binding on the applicability of specific mathematical techniques. The French philosopher-mathematician Rene Thom was invested in precisely this goal of making a mathematical technique like catastrophe theory so generally applicable that it becomes “substrate-neutral”.

But the merit of ‘mathematical philosophy’, as opposed to the philosophy of mathematics, is problematized further because it seems such a philosophy would privilege an intuitive understanding of mathematical 'notions' over the development of new mathematical structures which would actually embody the promised levels of generalities. By demonstrating the insights gained from Rene Thom regarding the literary structure of narratives, I will ask if such a substrate-neutral mathematical philosophy actually amounts to mathematics as we typically identify it? Would we be convinced that there could be an authentic mathematical philosophy emerging out of, but not encumbered by the practice of mathematics as such?

Brief Bio:     Ravi Sekhar Chakraborty is pursuing doctoral research in philosophy at IIT Delhi before which he studied English literature and mechanical engineering. He is working in the intersection of philosophy of mathematics and philosophy of literature.

Title:    Analytics in Healthcare

Speaker:    Mahesh Iyer, Co-founder, Sineflex Solutions

Date:    February 7, 2020 (Friday)

Abstract:     Healthcare has typically been a laggard when it comes to adopting new technologies, and analytics is no exception. There have been many reasons for this... the most commonly used one is that the healthcare domain is most stringently regulated. However, this is only the tip of the iceberg, there are many more reasons for the slow uptake of emerging technologies in healthcare. However, this trend is changing, and today, healthcare is seen to be embracing the newer technologies with open arms. During this talk, we will discuss some of the use cases for the use of analytics in this domain, what is currently being done, and also discuss what are some of the challenges in making it work.

Brief Bio:     Dr. Mahesh Iyer is cofounder of Sineflex Solutions,LLP. He has more than 20 years of experience in R&D in healthcare. Before Sineflex, Dr. Iyer was at Novartis and worked on multiple roles including Site Head, Biostatistics at Hyderabad, and Global head for Exploratory Safety and Statistical Analytics. He has also worked at Bristol Myers Squibb and Boehringer Ingelheim. Dr. Iyer is constantly working on establishing industry academia col- laboration. He had set up one of the first part-time Ph.D. pro- gram in Statistics for Novartis associates and has taught at vari- ous institutes. He also helped start the BIRAC funded med-tech accelerator at the Centre for Innovation and Entrepreneurship, IIIT Hyderabad and is now the domain mentor of it. He is a certified coach in the areas of emotional intelligence, assessment centers, and psychometric evaluations. He has been on various panels to discuss on mentoring and communication skills. He is actively involved in Statistical communities. Currently he is pres- ident of both the International Indian Statistical Association, In- dia chapter and Indian Association for Statistics in Clinical tri- als.

Title:    Shape and Spectra

Speaker:    Acushla Saraswat, Department of Mathematics, IIIT-Delhi

Date:    January 17, 2020 (Friday)

Abstract:     We look at the relationship between the shape of a domain and the eigenval- ues/eigenfunctions of the associated Laplace operator. The motivation behind this study comes from the wave equation, which has many applications in real life. We will touch on this topic very briefly, to begin the discussion, and then proceed to the main topic, namely, shape and spectra. Some open problems in this area will also be mentioned during the course of the seminar. The talk should be accessible to students who have had undergraduate level exposure to real analysis, vector calculus and linear algebra.

Brief Bio:     Dr. Acushla Saraswat is a Lecturer in the Department of Mathematics at IIIT-Delhi. She obtained her Ph.D. in 2018 from the University of Mumbai. Her area of research is differential geometry, with specialization in shape calculus/ optimization.

Title:    Reasoning about Knowledge

Speaker:    Sankha Basu, Department of Mathematics, IIIT-Delhi

Date:    January 16, 2020 (Thursday)

Abstract:     The logic of knowledge or Epistemic Logic is a kind of modal logic. In this talk, I will very briefly describe a modal logic and then move on to single-agent epistemic logic. Following this, I will describe multi-agent epistemic systems, where in addition to knowledge of individual agents, we can consider group knowledge, distributed knowledge, and common knowledge of a group of agents. In the third and last part of this talk, I will briefly talk about the motivations for a bimodal system introduced by Dabrowski, Moss, and Parikh in 1992, called topologic, which connects topology with epistemic logic and is useful as a framework for reasoning about a notion of effort in epistemic logic.

Brief Bio:     Dr.SankhaS.Basu is an AssistantProfessor in the Department of Mathematics at IIIT-Delhi. He obtained his Ph.D. degree in Mathematics from Pennsylva- nia State University in 2013. His area of research is Mathematical Logic and Foundations of Mathematics.

Title:    Kant and Husserl on the Question of `Transcendental' Logic

Speaker:    Nishad Patnaik, Department of Social Sciences and Humanities, IIIT-Delhi

Date:    January 16, 2020 (Thursday)

Abstract:     This talk argues that Kantian transcendental idealism and Husserlian phenomenology are distinct yet structurally analogous responses to the positivistic restriction of reason, initially encountered in the formal logics of their times. Through an examination of the Kantian and Husserlian critique of Aristotelian and truth-functional logic respectively, I claim that despite the difference in these logics, hence, distinct articulations that their transcendental critiques take, this structural anal- ogy extends to the interconnected problems of: 1) ‘method’, or the correct point of departure for a transcen dental critique of logic and 2) restoring ‘intuitive content’ to formal logic; as two aspects of the same discursive movement of thought. The discussion underscores the recognitive, memo- rial and ultimately Spatio-temporal processes of experience that both Kant and Husserl bring to light, as irreducible elements, even in relation to the formal-logical articulation of reason.

Brief Bio:     Dr. Nishad received his PhD in philosophy from The New School for Social Research (NSSR), New York, U.S.A in 2013. He holds a M.A. in philosophy from NSSR, as well as a M.A. and M.Phil. in philosophy from Delhi University. His dissertation entitled, “Time, Space and Finitude; Kant and Husserl on the Question of Transcendental Logic” received the ‘Alfred Schutz Memorial Award in Philosophy and Sociology’. In addition to his research interests in Kantian transcendental Idealism, and Husserlian phenomenology, Nishad’s other areas of research include Social and Political Philosophy, Marx and the Critical Theory tradition, Ethics, and the Philosophy of Technology. He is currently engaged in writing a book length manuscript on the genealogy of nationalist identity and its apparently paradoxical reassertion in the context of the hegemony of the contemporary capitalist world order.

Title:    Regular Bernstein Blocks

Speaker:    Manish Mishra, Assistant Professor, Indian Institute of Science Education and Research (IISER), Pune

Date:    January 10, 2020 (Friday)

Abstract:     I will recall some standard results of Bernstein in the representation theory of p-adic reductive groups. I will review the theory of Bernstein center and explain the Bernstein decomposition of the category of smooth representations of a p- adic group. I will then present an approach for understanding Bernstein blocks and state some of our results in that direction. This is a joint work with Jeffrey Adler.

Brief Bio:     Dr. Manish Mishra is an Assistant Professor of Math- ematics at the Indian Institute of Science Education and Research (IISER), Pune, India. He previously held postdoctoral positions at the Heidelberg University and the Hebrew University of Jerusalem. He com- pleted his B.Tech at the Indian Institute of Technology Kanpur and his Ph.D at Purdue University, USA.

Title:    Discretizations of Exterior Calculus and Differential Geometry?

Speaker:    Anil N. Hirani, Associate Professor, Department of Mathematics, University of Illinois at Urbana-Champaign

Date:    January 3, 2020 (Friday)

Abstract:     Exterior calculus on manifolds generalizes vector calculus to smooth manifolds. Real-valued dif- ferential forms are the main objects. Vector bundles with connections are a further generalization, with vector bundle valued forms as the main objects. Exterior calculus is suitable for most partial differential equations of engineering physics and vector bundles with connections are suitable for differential geometry and most differential equations of mathematical physics. In computations, manifolds can be approximated by piecewise linear simplicial approximations. I will describe a discrete combinatorial theory of discrete exterior calculus (DEC) and its recent generalization to discrete vector bundles with connections. The main operator we develop is a discrete covariant exterior derivative that generalizes the discrete exterior calculus operator of DEC and yields a discrete curvature and a discrete Bianchi identity. In the first part of the talk I will describe DEC and its applications to the Hodge-Laplace problem and Navier-Stokes equations on surfaces, and then I will develop the discrete covariant exterior derivative and its implications. DEC is joint work with several collaborators over the years, with Kaushik Kalyanaraman being a major collab- orator. The newer work on discrete vector bundles with connection is joint work with Daniel Berwick-Evans and Mark Schubel.

Brief Bio:     Dr. Anil N. Hirani obtained his undergraduate degree from Birla Institute of Technology and Science (BITS), Pilani and M.S in Computer Science (Theoretical track) from Stanford University. He obtained his Ph.D. in Computer Science with minors in Math- ematics and Control and Dynamical Systems from California In- stitute of Technology (Caltech) in 2003. Dr. Hirani is currently an Associate Professor of Mathematics at University of Illinois at Urbana-Champaign. His work broadly encompasses Geometry and Topology (applied and computational), Numerical Analysis, and Computational Physics.