Annual Progress seminar

Wed, 28 Feb 11:00 am -12:00 pm

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Venue: Ramanujan Hall

Host: Suresh Kumar

Speaker: Vikrant Desai (174093013)

Title: Mean field games with degenerate diffusions

Abstract: We study mean field games with degenerate diffusions. We prove

the existence of a mean field equilibrium for class of mean field games with state dynamics given by controlled degenerate diffusions.

Abstract: In this seminar, we discuss three types of Kirchhoff-type PDE with memory involving usual time derivative, fractional time derivative, and fractional Laplacian. In the first half, we focus on well-posedness and regularity results. Then, we derive a semi-discrete error analysis of Galerkin FEM by defining a modified Ritz-Volterra projection  operator.  Finally, we develop fully discrete formulations and implement some examples to validate the proven theoretical results.

Abstract: In the first half of the talk, I will introduce key ideas and methodologies of causal inference in the scientific foundations of evidence-based medicine. I will trace the history (20th century) of modern drug development through the evolution of the law known as The Food, Drugs and Cosmetic Act. The law was instituted and further evolved in response to some major global health events/crises. The US Congress gave sweeping powers to the FDA to interpret and execute the law to develop a drug approval process based on empirical data and science. We will also trace the law’s impact on global drug policies. In that context, we will discuss ‘adequate and well-controlled studies and the role of statistics in the process. We will discuss some of the important examples on the way. 

Bio of the speaker:  As a statistician, I worked in academia, the federal government, and the Biotechnology/Pharma industry. I was in leadership and supervisory positions in the government (Department of Biostatistics at Center for Drug Development and Research, Food and Drug Administration), and in the pharma industry at Johnson & Johnson  (large pharma), Amgen (mid-size pharma when I began there) and Esperion (small biotech). The early years of my career (about 10 years) were in academic positions starting as a lecturer at Bombay University followed by several years at the University of California, Santa Barbara with a brief sojourn to IIT, Mumbai. I continued methodological research and publishing during my time in the government and industry as well. Currently, I offer statistical and regulatory consulting services to pharmaceutical companies specializing in strategic and secondary review of submission modules, DMC statistical membership, strategic reviews of protocols, and statistical analysis plans mostly in dermatology, immunology, cardiovascular, and antiviral therapeutic areas.  I am an elected Fellow of the American Statistical Association.

Abstract: The classical theorem of Beckman and Quarles states the following: A function from the Euclidean plane to itself that preserves unit distances must preserve all distances. We will discuss some key steps of the proof. We will also discuss our recent result generalizing this theorem. This is joint work with Ben Schmidt. We will try to make the talk accessible to a wide audience.