Lecture series on Hodge Theory

8 Nov., Wed.  at 11.30 am
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Venue: Ramanujan Hall

Host: Sudarshan Gurjar

Speaker: V. Srinivas, IIT Bombay

Title: Some elements of variation of Hodge structures

Abstract: I will touch on some aspects of variations of Hodge structure, finishing up my series of lectures for this semester.

Combinatorics and TCS Seminar

Wednesday, 8th Nov. 2.30 pm

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Host: Niranjan Balachandran

Venue:  Ramanujan Hall

Speaker: Venkitesh (University of Haifa, Israel)

Title: List Decoding Randomly Punctured Polynomial Ideal Codes
Abstract: List decoding is a paradigm in algorithmic coding theory, where for a received word (possibly corrupted to some extent), the objective is to efficiently obtain a small list of 'approximately correct' codewords. A classic problem in this context is to obtain constructions of 'polynomial-based' codes that can be optimally list decoded (up to the information-theoretic limit), with optimal field size and output list size.  Such codes will be said to 'achieve list decoding capacity'. While no such 'perfectly optimal' explicit constructions are known as yet, it has been observed in previous works that a promising trick of 'folding' codewords enables achieving capacity (non-optimally in other parameters), prominently at the cost of a blow-up in the folding size as the 'gap to capacity' approaches zero.  Some recent previous works showed a breakthrough where 'unfolded' polynomial codes (called Reed-Solomon codes) achieve capacity under a random choice of evaluation points.  We observe a similar result in the folded setting, with the folding size, held constant (independent of the gap to capacity), and for a much larger class of 'polynomial ideal codes'.  This talk is based on an ongoing joint work with Noga Ron-Zewi and Mary
Wootters.

CACAAG Seminar

Wednesday, 8 Nov. 5:30 pm

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Venue: Ramanujan Hall.

Host: Madhusudan Manjunath.

Speaker: Trygve Johnsen. 

Affiliation: The Arctic University of Norway.

Title: Geometry of matroids, with a view toward application in coding theory.

Abstract: We will try to explain some of the material in "Matroid Theory for Algebraic Geometers" by Erik Katz, and "Simplicial Generation of Chow rings of Matroids" by Bachman, Eur & Simpson. Here one associates geometric objects like toric varieties with matroids and describes the fans that give rise to them.  One also describes Chow rings of matroids, and how the (Bergman fan of a ) matroid itself can be viewed as an element of the Chow ring, or Minkowski weight,  for a (usually) "larger " uniform matroid.  If time permits, we will mention briefly how Chow rings can be defined also for q-matroids, an object arising from rank metric codes, analogous to how usual matroids are a tool to describe codes with the Hamming distance.