Program

Conference (January 21st -- January 28th 2022) 

The conference talks will take place online due to the current sanitary situation. They will take place at 7pm and 8.10pm IST time on January 21st, and 24th-28th.

The zoom link for lectures is the following:

• https://cmi-ac-in.zoom.us/j/82451019566?pwd=YXNrdHhqRTNkRmhidVhHSzZQSWdtZz09

The detailed planning is the following (IST time given). Lectures were also added to the online calendar.

• January 21st
• 7pm -- 8pm: Nitin Saxena (background talk) -- Paradigms for bounded top-fanin depth-4 circuits
• 8.10pm -- 9.10pm: Christian Ikenmeyer (background talk) -- Multiplicity obstructions
• January 24th:
• 7pm -- 8pm: Visu Makam (background talk) -- Exponential degree lower bounds for invariant rings
• 8.10pm -- 9.10pm: Nitin Saxena -- Demystifying the border of depth-3 algebraic circuits
• January 25th:
• 7pm -- 8pm: Christian Ikenmeyer -- On the separation of orbit closure via symmetries
• 8.10pm -- 9.10pm: Bharat Adsul (background talk) -- Affine vs projective orbit closures, Lie algebra actions and constructions.
• January 26th:
• 7pm -- 8pm: Pascal Koiran -- Tensor rank and commuting matrices: the case of real symmetric decomposition
• 8.10pm -- 9.10pm: Visu Makam -- How to prove orbits are closed?
• January 27th:
• 7pm -- 8pm: Milind Sohoni -- Lie algebra methods for projective limits of stable points
• 8.10pm -- 9.10pm: Pranjal Dutta -- Exponential-gap fanin-hierarchy for border depth-3 circuits
• January 28th:
  • 7pm -- 8pm: Markus Bläser -- Irreversibility of tensors of minimal border rank and barriers for fast matrix multiplication
  • 8.10pm -- 9.10pm: Thomas Seiller -- Invariants for group actions, logic and complexity

Online Lectures (August 24th -- December 17th 2021) 

These are planned every week on Tuesday and Friday at 7am Pacific Daylight Time (PDT). Four different themes will be covered, which we detail below. Here is a list of speakers for the online lectures. Note that some local pertubations to the calendar are possible. The precise planning is shown on the online calendar (or the text version) which will be kept up-to-date during the semester.

Warning: the Zoom link to attend online lectures have changed; please check your email or the information provided in the online calendar.

Algebraic Geometry

Definitions of affine and projective varieties, class varieties associated to complexity classes, coordinate rings of varieties, local rings at points, normality and smoothness, representation theory of GL(n), GL(n) modules in coordinate rings of class varieties, early conjectures of GCT, update on the conjectures.

Algebraic Groups

GL(n) action on vector spaces and affine varieties, Chevalley's theorem, algebraic Peter-Weyl theorem, reductivity, Matsushima's theorem,GL(n) action on projective varieties, invariants, null cone, semistability, Hilbert Mumford criterion, GIT quotients, moment map and symplectic quotients, Kempf Ness theorem, moment polytopes.

Optimization

Gradient descent algorithm, analysis assuming convexity, left right action, moment map and capacity (abelian case), torus actions and linear programming, alternate minimisation algorithm, moment map - non abelian setting, geodesic convexity, parameters from representation theory arising in the analysis of convergence, geodesic optimization, algebraic algorithms for left right action, algorithms for left right action using discrete convex optimization over Euclidean buildings.

Algebraic Complexity Theory

Arithmetic Circuit Model (and its generality subsumes models with division, square roots, etc.), Circuit subclasses (Formulas and Branching Programs), Open Problems (VP versus VNP and its relation to P vs NP and #P vs NC, PIT, Matrix Multiplication), Iterated Matrix Multiplication and other Upper Bounds, Depth reduction and structural results (homogenization/(set) multilinearization), Lower Bounds (Monotone lower bounds, Partial derivatives, General template for lower bounds), Polynomial Identity Testing and its relationship to other problems (Heintz-Schnorr and Forbes-Shpilka), Reconstruction and its applications (coding theory, tensor decomposition) and reconstruction of simple classes (Sparse Interpolation, Polynomial Factorization and reconstruction of other simple classes, general template for reconstruction)