Homepage: https://sites.google.com/view/pduttashomepage

Dr. Pranjal Dutta (https://sites.google.com/view/pduttashomepage) is currently a Research Fellow (Postdoc) at the School of Computing, NUS hosted by Prof. Divesh Aggarwal. His broad research area is Complexity theory. He finished his PhD in Computer Science (2018-2022), from Chennai Mathematical Institute (CMI), under the guidance of Prof. Nitin Saxena (IIT Kanpur). He is the winner of the ACM India Doctoral Dissertation Award 2023. During his PhD, he was a recipient of the Google PhD Fellowship (2018 -2022). He has recently been awarded the Simons-Berkeley Research Fellowship and will be spending Fall 2025 at UC Berkeley.

AG 1   Info

AG Audience

English

30 Minutes

Saarbrücken

Border complexity of polynomials plays a crucial role in the Geometric Complexity Theory (GCT) approach to separating P from NP. Defined via limits or topological closures, border complexity captures functions that can be approximated arbitrarily closely by low-complexity functions. Debordering refers to the task of proving upper bounds on non-border complexity measures in terms of border complexity measures, effectively eliminating the need for limits. A classical example of debordering is Bini's result on matrix multiplication tensors, which was instrumental in the development of fast matrix multiplication algorithms. However, despite its significance, only a handful of debordering results are currently known. In this talk, I will survey recent progress in debordering and their implications for algebraic complexity theory.

Nidhi Rathi

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