From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford, June 1-2

From June 1-2, the Center of Mathematic Sciences and Applications will host a conference on From Algebraic Geometry to Vision and AI:  A Symposium Celebrating the Mathematical Work of David Mumford. The event will be held in the Harvard Science Center, Hall D.

Please click here to register for this event. 

Confirmed speakers and panelists:


Schedule:

Please note that the schedule for both days is currently tentative and is subject to change.

June 1, Thursday (Full day)

On Algebraic Geometry

Time Speaker Topic
9:00am – 9:05am Opening
9:05am – 9:55am János Kollár Title: Moduli spaces of algebraic varieties

Abstract: The aim of the talk is to discuss how Mumford’s works on the moduli of curves developed into the current moduli theory of higher dimensional varieties.

10:10am – 11:00am Peter Scholze Title: Relating arithmetic and geometry

Abstract: Based on computations of Galois cohomology, an analogy between the spectra of (rings of integers of) number fields and 3-manifolds has been observed in the 60’s by Mumford and others. This analogy relates in particular the absolute Galois groups of number fields with the fundamental groups of 3-manifolds. This analogy remains mysterious, but there are some isomorphisms between absolute Galois groups and fundamental groups of geometric objects, which the talk aims to summarize.

11:00am – 11:30pm Tea Break
11:30am – 12:20pm Aaron Pixton Title: The tautological ring

Abstract: The tautological ring of the moduli space of smooth curves
was introduced by Mumford in the 1980s in analogy with the cohomology of Grassmannians. I will discuss what is now known (or still unknown) about the structure of this ring.

12:20pm – 2:00pm Lunch
2:00pm – 2:50pm Burt Totaro Title: Rationality and algebraic cycles

Abstract: We survey the recent applications of the theory of algebraic cycles to the problem of determining which algebraic varieties are rational or stably rational.

3:05pm – 3:55pm Avi Wigderson Title: Invariant theory and computational complexity

Abstract: I will discuss recent work in which degree bounds on
invariant rings play an essential role in the efficiency analysis of Gurvits’ “operator scaling” algorithm (a quantum generalization of Sinkhorn’s “matrix scaling” algorithm). This algorithm is motivated from problems in algebraic complexity theory and non-commutative algebra, and turns out to have applications in optimization and analysis. Based on joint work with Garg, Gurvits and Olivera.

3:55pm – 4:25pm Tea Break
4:25pm – 5:40pm Panel on “Shape” with David Gu, L. Mahadevan, Peter Michor, Michael Miller; moderated by Barry Mazur

June 2, Friday (Full day)

Geometry, Vision, and AI

Time Speaker Topic
9:00am – 9:10am Yang Wang Opening
9:10am – 9:35am Jayant Shah TBA
9:35am – 10:00am Sol Garfunkel TBA
10:00am – 10:25pm Persi Diaconis TBA
10:25am – 10:45am Tea break
10:45am – 11:10am Michael Miller Brain mapping
11:10am – 11:35am Laurent Younes TBA
11:35am – 12:00am Tai-Sing Lee Neuroscience
12:00pm – 2:00pm Lunch break
2:00pm – 2:25pm David Gu Title: Discrete Optimal Mass Transportation for Shape Classification

Abstract: We introduce a variational approach for solving discrete optimal mass transportation problem. The method is equivalent to solve Monge-Ampere equation and applied for 3D shape classification using Wasserstein distance.

2:25pm – 2:50pm Ying Nian Wu Stat models of visual patterns and learning
2:50pm – 3:15pm Stuart Geman Grammars and vision
3:15pm – 3:35pm Tea break
3:35pm – 4:00pm Josh Tenenbaum Cognitive AI
4:00pm – 4:25pm Song-Chun Zhu Title: A Cognitive Architecture for  Human-Robot Collaboration

Abstract: In this talk, I will demonstrate ongoing efforts for developing autonomous robots that can collaborate with humans in real world scenes and tasks. Our cognitive architecture embraces modern progresses in vision, cognition, learning, NLP with a unified knowledge representation — the spatial, temporal and causal and-or graph (STC-AOG). The STC-AOG is a probabilistic, graphical and compositional model that represents stochastic context sensitive grammars for the hierarchical structures in scenes and objects (spatial), in events and actions (temporal), and in the effects of actions on the scenes (causal). The architecture also consider the theory of minds, i.e. the beliefs and intents of multi-agents, and their shared beliefs and plans for collaborations.

4:25pm – 4:50pm Mark Nitzberg TBA

Organizers include:

For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

*This event is jointly supported by the CMSA, National Science Foundation, and the International Science Foundation of Cambridge.

 

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