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Published on : 18/09/201929/01/2021 Published by : Administrator

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Congratulations to Assistant professor Max Gurevich for receiving The Kurt Mahler Prize Fund in Mathematics for the published paper: "On restriction of unitarizable representations of general linear groups and the non-generic local Gan–Gross–Prasad conjecture."
The paper is part of a quest for understanding branching laws that govern restriction of representations (linear actions) of a group to a lower-rank subgroup.
These are curious mathematical phenomena that sometimes appear in a physical context of symmetry breaking.

The elegant classical case, where simple combinatorial branching laws fully determine the spectral behavior of the restriction operation, is that of finite permutations groups.
Given an irreducible linear action (a building block for a symmetry of a given type) of the group of permutations on n symbols, restriction to the smaller subgroup of permutations on n-1 symbols will render the irreducible situation into a reducible one. In other words, the original building blocks will now decompose into smaller ones.
All of these 'blocks' have combinatorial 'names' - they may be described by possible partitions of the integer n (or n-1). Hence, branching laws describe how a given partition decomposes into
partitions of a smaller integer.
This is a good example for one of the strengths of Lie theory, which attempts to describe continuous symmetries, that often appear in nature, through discrete terms that would be easier for us to grasp.

In his studies, the groups are infinite, coming from symmetries inherent in number theory. Their representations are infinite-dimensional, and things can become tough... In fact, general branching problems like the one described above for finite groups are considered in this setting too 'wild' to admit a short and inclusive solution. Yet, recent years have seen some progress on the matter.

In this paper exhibits new techniques for identifying branching laws for representations in a special class that naturally appears in number theory. As an application, they have affirmed cases of an emerging system of conjectures (Gan-Gross-Prasad), which is a leading promising direction in the wide effort of connecting geometry with number theory.

Read more in the full version of the paper:
https://lnkd.in/dE2w2TAM

Learn more about Max and his research: https://lnkd.in/dqeDU2VQ ... See MoreSee Less

2 weeks ago

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We welcome Associate professor Yuval Filmus from The Henry and Marilyn Taub Faculty of Computer Science at the Technion as our new Faculty member (secondary appointment).
Yuval specializes in three central areas: combinatorics, analysis of Boolean functions, and computational complexity.
In the last several years, his research has focused on circuit complexity, propositional proof complexity, communication complexity, and fast matrix multiplication.
For further information, go to his personal website: https://yuvalfilmus.cs.technion.ac.il/ ... See MoreSee Less

4 weeks ago

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The Faculty of Mathematics at the Technion will hold its yearly student event, Exposure to Mathematical Research.
We are inviting all curious undergraduate students (finishing their 2nd and 3rd year of mathematical studies) to register.
Participants will have an opportunity to learn about some of the current challenges in mathematical research and to experience first-hand the type of work done by modern-day mathematicians.
The main program will consist of projects in small groups of 2-4 students, guided by faculty members and postdoctoral associates from the Faculty of Mathematics and exploring a topic of current interest.
The program will also include social gatherings and other activities.
Housing, meals, and a stipend will be provided.
We look forward to meeting you and sharing our excitement for mathematical research and exploration!
For the list of projects, mentors and registration, go to: https://lnkd.in/eGJhHA9W ... See MoreSee Less

2 months ago

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