Theoretical Statistics and Mathematics Unit

Seminar and Colloquium of the week


Title :Polynomial indexing of the lattice points
Speaker : M.A. Vsemirnov (Russian Academy of Sciences - St. Peterburg)
Time : January 24, 2019 (Thursday), 03:30 PM
Venue : Auditorium
Abstract : While studying cardinalities of sets, G. Cantor introduced two polynomials that gave bijections between $N^2$ and $N$. Are there other polynomials with the same property? This problem still remains open. In my talk, I shall survey known partial results and discuss some multidimensional analogues.


Title : On friendly cats and dogs
Speaker : Bhaskar Bagchi (ISI Bangalore)
Time : January 29, 2019 (Tuesday), 03:15 PM
Venue : Auditorium
Abstract : In a certain house, there are a number of cats and dogs. Any two of the cats have exactly two common friends among the dogs, and any two of the dogs have exactly two common friends among the cats. Question : what is the maximum possible number of dogs in this house? It may sound like a silly puzzle, but I conjecture that there can be a maximum of 79 dogs here. I shall discuss the surprising mathematics into which I am led in trying to solve this puzzle.


Title :Distributions of maxima of quadratic forms and homogeneous functions of Gaussian random vectors
Speaker : Vladimir Bogachev (Moscow State University and Higher School of Economics)
Time : January 31, 2019 (Thursday), 03:30 PM
Venue : Auditorium
Abstract : We discuss conditions for the uniform boundedness of distribution densities and boundedness of their variations for several types of functions of Gaussian random vectors. Our examples include maxima of several quadratic forms, homogeneous functions and convex functions. Some new results will be presented that give bounds for distribution densities and their variations with a particular emphasis on estimates independent of the dimension of the given Gaussian vector.

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