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