From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford

On August 18 and 20, 2018, the Center of Mathematic Sciences and Applications and the Harvard University Mathematics Department will host a conference on From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford. The talks will take place in Science Center, Hall B.

 Saturday, August 18th:  A day of talks on Vision, AI and brain sciences
 Monday, August 20th: a day of talks on Math

The full schedule for this event, including talk titles and abstracts, will be posted here when available.

Speakers:

Organizers:

Please register here. 

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

 

Saturday, August 18, 2018

Human and machine Intelligence: Geometry, Vision and AI

Time Speaker Title/Abstract
8:30 – 9:00am Breakfast
9:00 – 9:20am Symposium Kickoff
History and Perspectives
9:20 – 9:45am Jayant Shah Northeastern Title: The accuracy of solar eclipse prediction in ancient and medieval astronomy

Abstract: Predicting solar eclipses was one of the important challenges in ancient and medieval astronomy. Using a statistical approach, David Mumford tested the accuracy of the Chinese algorithm for predicting solar eclipses as formulated in Shoushili. Using David’s code, I have carried out a similar analysis of the Indian Tantrasangraha and the Greek Almagest. In this talk, I will describe the method and compare the accuracy of the three algorithms.

9:45 – 10:10am     Bernard Saint-Donat Saint-Donat & Co.
10:10 – 10:30am Break
10:30 – 10:55am Yang Wang USTHK
10:55 – 11:15am Break
Brain, Neural and Cognitive Sciences
11:15 – 11:40 Michael Miller  Johns Hopkins Title: Brain mapping
11:40 – 1:40pm Lunch
1:40 – 2:05pm Tai Sing Lee CMU Title: Neuroscience
2:05 – 2:30pm Josh Tenenbaum  MIT Title: Cognitive AI
Vision and Pattern Theory
2:30 – 2:55pm Peter Belhumeur Columbia Title: Computer Vision
2:55- 3:15pm Break
3:15 – 3:40pm Stuart Geman Brown Title: Grammars and vision
3:40 – 4:00pm Coffee break
4:00 – 4:25pm Yingnian Wu UCLA Title: Stat models of visual patterns and learning
4:25 – 4:55pm Jitendra Malik Berkeley / FAIR
4:55 – 5:25pm Song-Chun Zhu UCLA
5:25 – 5:55pm Q&A

Monday, August 20, 2018

Algebraic Geometry and Shape

Time Speaker Title
9:00 – 9:05am Opening
9:05 – 9:55am Janos Kollar Princeton Moduli spaces of algebraic varieties
9:55 – 10:10am Break
10:10 – 11:00am Emanuele Macri Northeastern Title: Bridgeland stability and applications

Abstract: One of the key ideas in the theory of derived categories, due to Bondal and Orlov in the 90’s, is that the derived category of coherent sheaves on a smooth projective variety should contain very important information on the geometry of the variety itself, for example on its birational properties.

A conjectural way to obtain such information is via the theory of moduli spaces of objects in the derived category, generalizing the existing theory of moduli spaces of vector bundles developed by Mumford, Narasimhan, Seshadri, Gieseker, Maruyama, and Simpson, among others. In 2003, motivated by previous work in High Energy Physics by Douglas, Bridgeland introduced the notion of stability condition for derived categories; this allows to define and study such moduli spaces of objects.

In this talk, I will give an introduction to Bridgeland’s theory, focusing in particular to applications of the theory to problems in Algebraic Geometry. For instance, I will present Bayer’s new proof of the Brill-Noether Theorem and a new proof for a theorem of Gruson-Peskine and Harris on the genus of space curves (which is joint work with Benjamin Schmidt).

11:00 – 11:30am Break
11:30 – 12:20pm Aaron Pixton MIT “The tautological ring”
12:20 – 2:10pm Lunch
2:10 – 3:00pm Burt Totaro UCLA Rationality and algebraic cycles
3:00 – 3:10pm Break
3:10 – 4:00pm Avi Wigderson Princeton Optimization, Computational Complexity and Invariant Theory (to be confirmed)
4:00 – 4:30pm Break
4:30 – 5:20pm Peter Michor Vienna “Shape spaces” alias “Moduli spaces in the differentiable category”