Anish Ghosh receives the 2021 Shanti Swarup Bhatnagar Prize

Anish Ghosh has received the 2021 Shanti Swarup Bhatnagar Prize in Mathematical Sciences. The Shanti Swarup Bhatnagar Prize is India’s highest science award within the country. While at Brandeis, Anish Ghosh was the student of Dmitry Kleinbock, Professor of Mathematics. He is currently a faculty member at the Tata Institute of Fundamental Research (TIFR), Mumbai where he specializes in Ergodic Theory and Number Theory.

Kleinbock wrote the following about his former student:

“It was a great pleasure to find out that Anish Ghosh, my former student here at Brandeis, has received the Shanti Swarup Bhatnagar prize. Anish is a talented mathematician working in the field of ergodic theory on homogeneous spaces. Interest in this field rose significantly during the late 1980s and early 1990s after the seminal achievements of Marina Ratner and Anish’s mathematical grandfather Gregory Margulis, whose work, in particular the proof of the Oppenheim Conjecture, has since served as a basis for numerous links between dynamics and number theory.”

“Anish has been exploring connections between the two fields throughout his mathematical career. Since his graduation in 2006 he has authored more than 40 papers, many published in top-level journals, and has become one of a few people who are shaping the subject of ergodic theory and its arithmetical applications. Among his notable achievements I can mention the work on distribution of dense lattice orbits in homogeneous spaces, on intrinsic Diophantine approximation, on applications of equidistribution to counting lattice points and – most recently – an approach to quantitative Oppenheim-type problems involving Rogers’ moment formulas.”

“Anish has also been a great mentor, who as of now has produced at least 8 PhD students and collaborated with them extensively on various problems. He has lectured extensively on the subject of connections of dynamics and number theory and edited several collections of papers. To summarize, the Bhatnagar Prize is well deserved, and I am positive that the mathematical talent of Anish Ghosh will continue to flourish.”

Why do so many powers of 2 start with “1”?

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384 …

If you liked math in middle school, odds are that maybe you memorized the powers of two. But did you ever think about the fact that so many of them start with the digit “1”? Is there a reason for it? How would you go about stating the problem in more formal mathematical terms?

Dmitry Kleinbock from the Brandeis Math department explains in this Numberphile video:

Be sure to watch the extra content (below) for a slightly more technical, but still completely approachable, additional explanation, where the problem reduces to the so-called equidistribution property of irrational rotations of the unit circle.

Are there other numbers more likely to start with the digit “1”?  It’s pretty easy to convince yourself that there are.

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