CMSA

Growth and zero sets of eigenfunctions and of solutions to elliptic partial differential equations
2019-02-25 09:30 - 2019-03-01 17:00 (America/New_York) | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
From February 25 to March 1, the CMSA will be hosting a workshop on Growth and zero sets of eigenfunctions and of solutions to elliptic partial differential equations.
Key participants of this workshop include David Jerison (MIT), Alexander Logunov (IAS), and Eugenia Malinnikova (IAS). This workshop will have morning sessions on Monday-Friday of this week from 9:30-11:30am, and afternoon sessions on Monday, Tuesday, and Thursday from 3:00-5:00pm.
The sessions will be held in (G02) (downstairs) at 20 Garden, except for Tuesday afternoon, when the talk will be in (G10).

2/22/2019 Social Science Applications Forum
2019-02-22 14:00

2/21/2019 Random Matrix and Probability Theory Seminar
2019-02-21 16:30 - 17:30

Optimally Imprecise Memory and Biased Forecasts
2019-02-20 16:30 - 17:30 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: Michael Woodford (Columbia)
Title: Optimally Imprecise Memory and Biased Forecasts
Abstract: We propose a model of optimal decision making subject to a memory constraint. The constraint is a limit on the complexity of memory measured using Shannon’s mutual information, as in models of rational inattention; the structure of the imprecise memory is optimized (for a given decision problem and noisy environment) subject to this constraint. We characterize the form of the optimally imprecise memory, and show that the model implies that both forecasts and actions will exhibit idiosyncratic random variation; that beliefs will fluctuate forever around the rational-expectations (perfect-memory) beliefs with a variance that does not fall to zero; and that more recent news will be given disproportionate weight. The model provides a simple explanation for a number of features of observed forecast bias in laboratory and field settings. [Joint work with Rava Azeredo da Silveira and Yeji Sung

2/20/2019 Fluid Dynamics Seminar
2019-02-20 15:00 - 16:00

2/14/2019 Random Matrix and Probability Theory Seminar
2019-02-14 16:30 - 17:30

2/14/2019 General Relativity Seminar
2019-02-14 15:00 - 16:00

2/13/2019 Special Algebraic Geometry Seminar
2019-02-13 15:00 - 16:00

2/13/2019 Hodge and Noether-Lefschetz Loci Seminar
2019-02-13 13:30 - 15:00

2/11/2019 Mathematical Physics Seminar
2019-02-11 12:00 - 14:00

2/7/2019 Random Matrix and Probability Theory Seminar
2019-02-07 16:30 - 17:30

Inference for the Mean
2019-02-07 16:30 - 17:30 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: Ulrich Mueller (Princeton)
Title: Inference for the Mean
Abstract: Consider inference about the mean of a population with finite variance, based on an i.i.d. sample. The usual t-statistic yields correct inference in large samples, but heavy tails induce poor small sample behavior. This paper combines extreme value theory for the smallest and largest observations with a normal approximation for the t-statistic of a truncated sample to obtain more accurate inference. This alternative approximation is shown to provide a refinement over the standard normal approximation to the full sample t-statistic under more than two but less than three moments, while the bootstrap does not. Small sample simulations suggest substantial size improvements over the bootstrap.

2/7/2019 General Relativity Seminar
2019-02-07 15:00 - 16:00

2/6/2019 Hodge and Noether-Lefschetz Loci Seminar
2019-02-06 13:10 - 15:00

Special Lecture Series on Derived Algebraic/Differential Geometry
2019-02-05 15:00 - 2019-06-09 16:30
In the Spring 2019 Semester, the CMSA will be hosting a special lecture series on Derived algebraic/differential geometry run by Artan Sheshmani, with lectures given by Prof. Sheshmani and Dr. Dennis Borisov. The seminar will be held on Tuesdays and Thursdays from 3:00-4:30pm in CMSA, room G10.

Click here for reference material
Click here for a syllabus
Schedule:
Section 1: Basic setting of derived geometry
The goal: To collect the minimum set of tools needed to do algebraic geometry in the derived context.

2/05/2019
Lecture 1: Model and с-categories
Video

2/07/2019
Lecture 2: Grothendieck topologies and homotopy descent
Video

2/12/2019
Lecture 3: Derived Artin stacks
Video

2/14/2019
Lecture 4: Cotangent complexes

Section 2: Loop spaces and differential forms
The goal: This is the algebraic heart of the course – here we learn the homological techniques that are needed for shifted symplectic forms.

2/19/2019
Lecture 5: De Rham complexes and S1-equivariant schemes (loop spaces)
Video

2/21/2019
Lecture 6: Chern character
Video

2/26/2019
Room G02
Lecture 7: Local structure of closed differential forms in the derived sense Part I
Video

2/28/2019
Lecture 8: Local structure of closed differential forms in the derived sense Part II
Video

3/05/2019
Lecture 9: Cyclic homology
Video

Section 3: Shifted symplectic structures
Goal: To see applications of the algebraic techniques from above in the geometric context of the actual moduli spaces.

3/07/2019
Lecture 10: Definition and existence results
Video

3/12/2019
Lecture 11: Lagrangians and Lagrangian fibrations
Video

3/14/2019
Room G02
Lecture 12: Lagrangians and Lagrangian fibrations
Video

3/26/2019
Lecture 13: Intersections of Lagrangians
Video

3/28/2019
Room G02
Lecture 14: Examples and applications 2 (Part I)
Video

4/02/2019
Lecture 15: Examples and applications 2 (Part II)
Video

Section 4: Uhlenbeck–Yau construction and correspondence

4/04/2019
Lecture 16: Examples and applications 2 (Part III)
Video

4/09/2019
Room G02
Lecture 17: Uhlenbeck–Yau construction and correspondence Examples (Part I)
Video

Colloquia & Seminars,Events,Seminars

2/4/2019 Math Physics Seminar
2019-02-04 12:00 - 14:00

1/31/2019 General Relativity Seminar
2019-01-31 15:00 - 16:00

1/30/2019 Hodge and Noether-Lefschetz Loci Seminar
2019-01-30 13:30 - 15:00

1/28/2018 Mathematical Physics Seminar
2019-01-28 00:00

1/27/2020 Math Physics Seminar
2019-01-26 00:00 - 2019-01-27 13:00

1/23/2019 Hodge Seminar
2019-01-23 13:30 - 15:00

Innovation in Cell Phones in the US and China: Who Improves Technology Faster?
2019-01-19 16:30 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: Richard B. Freeman (Harvard University and NBER)
Title: Innovation in Cell Phones in the US and China: Who Improves Technology Faster?
Abstract: Cell phones are the archetypical modern consumer innovation, spreading around the world at an incredible pace, extensively used for connecting people with the Internet and diverse apps. Consumers report spending from 2-5 hours a day at their cell phones, with 44% of Americans saying “couldn’t go a day without their mobile devices.” Cell phone manufacturers introduce new models regularly, embodying additional features while other firms produce new applications that increase demand for the phones. Using newly developed data on the prices, attributes, and sales of different models in the US and China, this paper estimates the magnitude of technological change in the phones in the 2000s. It explores the problems of analyzing a product with many interactive attributes in the standard hedonic price regression model and uses Principal Components Regression to reduce dimensionality. The main finding is that technology improved the value of cell phones at comparable rates in the US and China, despite different market structures and different evaluations of some attributes and brands. The study concludes with a discussion of ways to evaluate the economic surplus created by the cell phones and their contribution to economic well-being.

Geometric Analysis Approach to AI Workshop
2019-01-18 08:30 - 2019-01-21 17:30 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Due to inclement weather on Sunday, the second half of the workshop has been moved forward one day. Sunday and Monday’s talks will now take place on Monday and Tuesday.
On January 18-21, 2019 the Center of Mathematical Sciences and Applications will be hosting a workshop on the Geometric Analysis Approach to AI.
This workshop will focus on the theoretic foundations of AI, especially various methods in Deep Learning. The topics will cover the relationship between deep learning and optimal transportation theory, DL and information geometry, DL Learning and information bottle neck and renormalization theory, DL and manifold embedding and so on. Furthermore, the recent advancements, novel methods, and real world applications of Deep Learning will also be reported and discussed.
The workshop will take place from January 18th to January 23rd, 2019. In the first four days, from January 18th to January 21, the speakers will give short courses; On the 22nd and 23rd, the speakers will give conference representations. This workshop is organized by Xianfeng Gu and Shing-Tung Yau.
The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.
Speakers:

Sarah Adel Bargal, Boston University
Guy Bresler, MIT
Tina Eliassi-Rad, Northeastern
Yun Raymond Fu, Northeastern
Brian Kulis, Boston University
Na Lei, Dalian University of Technology
Yi Ma, UC Berkeley
Minh Hoai Nguyen, Stony Brook
Francesco Orabona, Boston University
Cengiz Pehlevan, Harvard SEAS
Tomaso Poggio, MIT
Zhiwei Qin, DiDi Research America
Kate Saenko, Boston University
Dimitris Samaras, Stony Brook
Johannes Schmidt-Hieber, University of Twente
Steven Skiena, Stony Brook
Vivienne Sze, MIT
Naftali Tishby, ICNC
Jiajun Wu, MIT
Ying Nian Wu, UCLA
Gangqiang Xia, Morgan Stanley
Eric Xing, Carnegie Mellon
Donghui Yan, UMass Dartmouth
Alan Yuille, Johns Hopkins
Juhua Zhu, Argus

1/16/2019 Hodge Seminar
2019-01-16 20:46

1/8/2019 Topology Seminar
2019-01-08 14:00

12/12/2018 Hodge Seminar
2018-12-12 20:43

12/10/2018 Topology Seminar
2018-12-10 20:43

12/10/2018 Mathematical Physics Seminar
2018-12-10 20:42

12/6/2018 Special Mathematical Physics Seminar
2018-12-06 20:45

Displacement convexity of Boltzmann's entropy characterizes positive energy in general relativity
2018-12-05 16:30 - 17:30 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: Robert McCann (University of Toronto)
Title: Displacement convexity of Boltzmann’s entropy characterizes positive energy in general relativity
Abstract: Einstein’s theory of gravity is based on assuming that the fluxes of a energy and momentum in a physical system are proportional to a certain variant of the Ricci curvature tensor on a smooth 3+1 dimensional spacetime. The fact that gravity is attractive rather than repulsive is encoded in the positivity properties which this tensor is assumed to satisfy. Hawking and Penrose (1971) used this positivity of energy to give conditions under which smooth spacetimes must develop singularities. By lifting fractional powers of the Lorentz distance between points on a globally hyperbolic spacetime to probability measures on spacetime events, we show that the strong energy condition of Hawking and Penrose is equivalent to convexity of the Boltzmann-Shannon entropy along the resulting geodesics of probability measures. This new characterization of the strong energy condition on globally hyperbolic manifolds also makes sense in (non-smooth) metric measure settings, where it has the potential to provide a framework for developing a theory of gravity which admits certain singularities and can be continued beyond them. It provides a Lorentzian analog of Lott, Villani and Sturm’s metric-measure theory of lower Ricci bounds, and hints at new connections linking gravity to the second law of thermodynamics. Preprint available at http://www.math.toronto.edu/mccann/papers/GRO.pdf
