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For the second semester, the seminar will meet every other Monday. The talks will take place from 10:00-10:45am in Schreiber 309. Light refreshments will be served at 9:30am, so you are encouraged to arrive early to socialize before the talk!
The TAU postdoc/graduate student seminar began in Fall 2021. The purpose of this seminar is for graduate students or postdocs to give colloquium-style talks on a topic of their choice: this could be about their research area or just something they think is interesting. All areas of math are welcome. Accessibility is emphasized and the atmosphere is relaxed, with discussion and questions encouraged. Department catering is provided, and there is time to socialize before and after the talk, with the goal of improving connections among junior mathematicians in the department.
If you would like to be added to (or removed from) the mailing list, please send me (Jacqueline) an email at jakqueline (at) mail (dot) tau (dot) ac (dot) il. Similarly, if you would like to give a talk, please send me an email.
Upcoming talks this semester:
April 11: Mike Roysdon (postdoc)
Topic: Some Inequalities in Convex Geometry
Description: In this talk we detail a survey of four fundamental inequalities which appear in convex geometry: the Brunn-Minkowski inequality, Rogers-Shephard inequality, Petty's projection inequality and Zhang's inequality. We will discuss how each inequality might be related, and if it's possible, we will discuss some extensions of these inequalities.
Please volunteer for future dates:
April 25
May 9
May 23
June 6
If you would like to give a talk but the exact timing is not perfect for you, or one of the other Mondays this semester would be better, please let me know. We have the room for every Monday between 9:00 and 11am, so we can make any time in that range work.
Past talks:
November 14: Jacqueline Warren (postdoc)
Topic: What is homogeneous dynamics?
Description: I will begin by explaining what homogeneous dynamics is, with a concrete example being in the space of lattices in R^2, which is identified with SL_2(R)/SL_2(Z). Then I will discuss how homogeneous dynamics can be used to understand problems in number theory, specifically Diophantine approximation. This talk will include some algebra, some number theory, and a little bit of analysis and geometry.
Further reading: Those who enjoyed the talk may find the following books interesting:
Ergodic Theory with a View Towards Number Theory by Manfred Einsiedler and Thomas Ward
Ratner's Theorems on Unipotent Flows by Dave Witte Morris
November 28: Gautam Aishwarya (postdoc)
Topic: Magnitude of metric spaces
Description: This talk will be about a new isometry-invariant notion of size of compact metric spaces called magnitude. I will define this quantity and survey some recent work in this area. We will focus on compact subsets of ℝn (under the 1-norm and the 2-norm) and relate magnitude to their other geometric invariants such as cardinality, volume, and dimension. Potential applications of magnitude to other mathematical objects admitting natural metric structures will also be discussed.
Further reading: Those who enjoyed the talk may find the following resources interesting:
The magnitude of a metric space: from category theory to geometric measure theory by Tom Leinster and Mark W. Meckes
December 12: Sittinon Jirattikansakul (postdoc)
Topic: An introduction to nonstandard analysis
Description: Nonstandard analysis, which was initiated by Robinson, is a concept in Calculus where the epsilon-delta definitions are replaced by 'infinitesimal'. It turns out to have some applications in additive combinatorics, graph theory, and Ramsey theory. In this talk, we will examine a nonstandard extension of the ordered field of real numbers, explain a construction of a nonstandard extension, and state some applications.
Further reading:
December 26: Zahi Hazan (PhD student)
Topic: Harmonic analysis over finite fields
Description: I’ll begin this talk by defining the Fourier transform for functions defined over a finite abelian group. I’ll show the analogs of Plancherel's theorem and of Fourier inversion formula. Then we'll focus on finite fields and introduce the Mellin transform. This will allow me to introduce the analog of Tate's local functional equation (1950).
If time permits, we will show how Tate's theory was extended to the general linear group GL(n) by Godement-Jacquet (1972), which, in turn, formed the foundations of the Langlands program.
Further reading:
J.T. Tate. Fourier Analysis In Number Fields and Hecke’s Zeta-Functions. PhD thesis, Princeton, 1950.
January 9: Zhuohui Zhang (postdoc)
Topic: Nilpotent orbits and Lie Group Representations
Description: In this talk, I will introduce the basics of certain geometric concepts in the geometry of flag varieties and the representation theory of Lie groups. I will also explain how these geometric concepts are related to some classical problems in linear algebra.
February 28: Daniele Garzoni (postdoc)
Topic: Finite groups of symmetries
Abstract: We will discuss symmetries of "finite" objects -- in modern terms, finite permutation groups. We will briefly recall the history of this subject, we will see some properties and many examples. Then, we will let character theory enter the picture. There are some nice interplays between permutation groups and character theory: One subject sheds light on the other, and vice versa. We will see some instances of this phenomenon. The seminar will be elementary and self-contained.
March 7: Zvi Shem-Tov (PhD student at the Hebrew University)
Topic: Khintchine-type theorems on manifolds: the convergence case for standard and multiplicative versions (following Bernick, Kleinbock and Margulis)
Abstract: I will state a problem concerning Diophantine approximation on manifolds and its solution due to BKM. This is a representable example where techniques from homogeneous dynamics are utilized for solving number theoretic problems. No special background in anything is required.
March 28: Omer Keshet (Masters student)
Topic: How to Disprove Provability Itself - Introduction to Set Theoretical Forcing
Description: In the 60's Paul Cohen Invented a method of proving that some statements in set theory are not provable, called forcing. He did this by assuming a proof exists, taking a small model of set theory (a set of sets that "acts like" the universe of sets) in which the proof holds, and forming from it a different model in which the statement is false. In this talk, we will define what "models of set theory" are, see the challenges arising from such objects, and see the outline of the forcing method in action with the famous Continuum Hypothesis. The talk assumes absolutely no prior knowledge in set theory (above first year undergraduate level).
If you enjoyed the talk, you may enjoy checking out "Set Theory - An Introduction To Independence Proofs" by Kenneth Kunen.