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Starting in 2021, PIMS has inaugurated a high-level network-wide colloquium series. Distinguished speakers will give talks across the full PIMS network with one talk per month during the academic term. The 2021 speaker series is part of the PIMS 25th Anniversary showcase.

Abstract: In The Hitchhiker’s Guide to the Galaxy, by Douglas Adams, the number 42 was revealed to be the “Answer to the Ultimate Question of Life, the Universe, and Everything”. But he didn’t say what the question was! I will reveal that here. In fact it is a simple geometry question, which then turns out to be related to the mathematics underlying string theory.

John Baez is a leader in the area of mathematical physics at the interface between quantum field theory and category theory, and has broad interests in mathematics, and science more generally. He created one of the earliest blogs "This week's finds in Mathematical Physics" (before the term blog existed!)

Baez did his PhD at MIT, and was a Gibbs Instructor at Yale before moving to University of California, Riverside in 1988.

Time:
All network wide colloquia take place at 1:30pm Pacific Time

Registration:
To attend this event please register here. Kindly note that this talk will be recorded.

Starting in 2021, PIMS has inaugurated a high-level network-wide colloquium series. Distinguished speakers will give talks across the full PIMS network with one talk per month during the academic term. The 2021 speaker series is part of the PIMS 25th Anniversary showcase.

The asymmetric exclusion process (ASEP) is a model of particles hopping on a one-dimensional lattice. While it was initially introduced by Macdonald-Gibbs-Pipkin to provide a model for translation in protein synthesis, the stationary distribution of the ASEP and its variants has surprising connections to combinatorics. I will explain how the study of the ASEP on a ring leads to new formulas for Macdonald polynomials, a remarkable family of multivariate polynomials which generalize Schur polynomials. In a different direction, the inhomogeneous ASEP on a ring is closely connected to Schubert polynomials, which represent classes of Schubert varieties in the flag variety. This talk is based on joint work with Corteel-Mandelshtam, and joint work with Donghyun Kim.

Speaker Biography: Lauren Williams is the Dwight Parker Robinson Professor of Mathematics at Harvard University and the Sally Starling Seaver Professor at the Radcliffe Institute. She is a leader in the field of algebraic combinatorics, with research programs on the positive Grassmannian, and combinatorial models in statistical mechanics. Before moving to Harvard, she was a professor at Berkeley, where she held numerous prestigious prizes and grants including a Sloan fellowship and an NSF Career grant. In a recent Quanta article on her work, she was described as fearless, for her willingness to take mathematical leaps.

Time:
All network wide colloquia take place at 1:30pm Pacific Time

Registration:
To attend this event please register here. Kindly note that this talk will be recorded.

Time:
All network wide colloquia take place at 1:30pm Pacific Time

Registration:
To attend this event please register here. Kindly note that this talk will be recorded.

Abstract:
Colour {1,..,N} red and blue, in such a manner that no 3 of the blue elements are in arithmetic progression. How long an arithmetic progression of red elements must there be? It had been speculated based on numerical evidence that there must always be a red progression of length about sqrt{N}. I will describe a construction which shows that this is not the case - in fact, there is a colouring with no red progression of length more than about exp ((log N)^{3/4}), and in particular less than any fixed power of N.

I will give a general overview of this kind of problem (which can be formulated in terms of finding lower bounds for so-called van der Waerden numbers), and an overview of the construction and some of the ingredients which enter into the proof. The collection of techniques brought to bear on the problem is quite extensive and includes tools from diophantine approximation, additive number theory and, at one point, random matrix theory.

Speaker Biography:
Ben Green works in additive combinatorics and related areas, such as harmonic analysis and approximate algebraic structure. The underlying relationship is that ideas rooted in harmonic analysis are used to give a quantitative description of randomness versus structure. Among many important results, the results with Terence Tao stating that the prime numbers contain arbitrarily long arithmetic progressions is a landmark. His work has revolutionized the field and Dr. Green has been awarded many prizes, including the Salem Prize and the Sylvester Medal of the Royal Society. Dr. Green is a Fellow of the Royal Society.

Ben Green is the Waynflete Professor of pure mathematics at the University of Oxford. Previously he was a Professor at the University of Cambridge. The paper with Terence Tao on arithmetic progressions in the primes was written when Ben Green was a PIMS postdoctoral fellow at the University of British Columbia.

About the PIMS Network-Wide Colloquia:
Starting in 2021, PIMS has inaugurated a high-level network-wide colloquium series. Distinguished speakers will give talks across the full PIMS network with one talk per month during the academic term. The 2021 speaker series is part of the PIMS 25th Anniversary showcase.

Description:
Starting in 2021, PIMS has inaugurated a high-level network-wide colloquium series. Distinguished speakers will give talks across the full PIMS network with one talk per month during the academic term. The 2021 speaker series is part of the PIMS 25th Anniversary showcase.

Abstract: Diffusion methods help understand and denoise data sets; when there is additional structure (as is often the case), one can use (and get additional benefit from) a fiber bundle model.

Time:
All network wide colloquia take place at 1:30pm Pacific Time

Registration:
To attend this event please register here. Kindly note that this talk will be recorded.