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“Compact Hyper-Kahler Manifolds in Algebraic Geometry”

Special Seminar

Come join us Wednesday January 24, 2018 at 12 pm in RM 507, Professor Giulia Sacca (MIT) will be giving a special lecture about “Compact Hyper-Kahler Manifolds in Algebraic Geometry”.


Hyper-Kahler (HK) manifolds appear in many fields of mathematics,
such as differential geometry, mathematical physics, representation theory, and
algebraic geometry.  Within algebraic geometry, compact HK manifolds appear
among the building blocks for algebraic varieties with trivial first Chern
class and as moduli spaces of vector bundles on K3 surfaces. The
distinguishing feature of compact HKs, whose role in algebraic geometry has
grown immensely over the last 20 years, is that they carry a holomorphic
symplectic form. This makes them the natural higher-dimensional analogues
of K3 surfaces.  In this talk I will give an overview of some of my work in
this field, including joint projects with some of the following collaborators:
E. Arbarello, J. Kollar, R. Laza, and C. Voisin.

Mathematics Hall, Room 507 at 12 pm




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“Rational Points in One-Parameter Families”

Special Seminar

Come join us Monday January 22, 2018 at 12 pm in RM 507, Professor Ari Shnidman (Boston College) will be giving a special lecture about “Rational Points in One-Parameter Families”.


How often does a “random” algebraic plane curve f (x , y) = 0 have a solution with rational coordinates? For one-parameter “twist” families of elliptic curves, Goldfeld conjectured that there is a rational point exactly half of the time. Recent progress towards this conjecture makes use of Selmer groups, and I’ll explain the simple geometric idea underlying their construction. I’ll also describe results for families of curves of higher genus and abelian varieties of higher dimension.

Mathematics Hall, room 507

Monday January 22, 2018 12 pm 

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“Understanding Number Fields Through the Distributions of their Arithmetic Invariants”


Come join us Friday January 19, 2018 at 12 pm in RM 507, Professor Ila Varma (Columbia University) will be giving a special lecture about “Understanding Number Fields Through the Distributions of their Arithmetic Invariants”


The most fundamental objects in number theory are number fields, field

extensions of the rational numbers that are finite dimensional as

vector spaces over Q. Their arithmetic is governed heavily by

certain invariants such as the discriminant, Artin conductors, and the

class group; for example, the ring of integers inside a number field

has unique prime factorization if and only if its class group is

trivial. The behavior of these invariants is truly mysterious: it is

not known how many number fields there are having a given discriminant

or conductor, and it is an open conjecture dating back to Gauss as to

how many quadratic fields have trivial class group.


Nonetheless, one may hope for statistical information regarding these

invariants of number fields, the most basic such question being “How

are such invariants distributed amongst number fields of degree d?”

To obtain more refined asymptotics, one may fix the Galois structure

of the number fields in question. There are many foundational

conjectures that predict the statistical behavior of these invariants

in such families; however, only a handful of unconditional results are

known. In this talk, I will describe a combination of algebraic,

analytic, and geometric methods to prove many new instances of these

conjectures, including some joint results with Altug, Bhargava, Ho,

Shankar, and Wilson.


Friday, January 19, 2018 at noon

Room 507, Mathematics Hall

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“Transport & Localization in Random Media: Theory & Applications”

This workshop will present recent developments on wave propagation, scattering and diffusion in random medias at the interface of probability theory, mathematical physics and PDEs. Accessible lectures by leading mathematicians will catalyze interactions among both junior and senior researchers in fundamental and applied fields.

Tuesday May 1 – 3, 2018

Organizers: Ivan Corwin, Alexis Drouot, Hao Shen, Michael I. Weinstein


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Wei Zhang awarded a New Horizons in Mathematics Prize

“Recognizing the Achievements of Early-Career Physicists and Mathematicians”

The New Horizons in Mathematics Prize is awarded to promising early-career researchers who have already produced important work in mathematics.

 Wei Zhang (Massachusetts Institute of Technology and Columbia University)

For more information please visit the link below;

Breakthrough Prize

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Simon Brendle awarded the 2017 Fermat Prize

“Results of researches accessible to the greatest number of professional mathematicians in fields where the contributions of Pierre de Fermat have been decisive (Statements of variational principles,  Foundations of probability and analytic geometry, Number theory)”

Simon A. Brendle (Columbia University, New York, USA) was awarded for his numerous and profound results in geometric analysis, involving partial differential equations of the elliptic, parabolic and hyperbolic type; in particular for his elegant proof of Lawson’s conjecture, for his characterization of soliton solutions of Ricci flows and mean curvature in dimension 3 as well as for his remarkable contributions, in collaboration with Gerhard Huisken, to the analysis of the flow of curvature average of convex surfaces on average in varieties of dimension 3.

The Fermat Prize 2017 ceremony will take place in spring 2018 in Toulouse, simultaneously with the presentation of the 2017 Fermat Junior Prize.

For more information please visit the websites below;

2017 Fermat Awards

Fermat Prize


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Nov 15:Russel Caflisch (Courant Institute, NYU)

Title: Signal Fragmentation for Low Frequency Radio Transmission
read more »

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CONGRATULATIONS to Professor Abouzaid!

Selection of the 2018 Fellows of the American Mathematical Society

Sixty three Mathematical scientists from around the world have been named Fellows of the American Mathematical Society (AMS) for 2018, the program’s sixth year and on November 1, 2017 Professor Mohammed Abouzaid was selected as one of the new AMS Fellows for 2018.

The Fellows of the AMS designation recognizes members who have made outstanding contributions to the creation, exposition, advancement, communication, and utilization of mathematics. Among the goals of the program are to create an enlarged class of mathematicians recognized by their peers as distinguished because of their contributions to the profession, and to honor excellence.

Regarding the new Fellows of the AMS program and the Society, AMS President Kenneth A. Ribet says,”This year’s class of AMS Fellows has been selected from a large and deep pool of superb candidates. It is my pleasure and honor as AMS President to congratulate the new Fellows for their diverse contributions to the mathematical sciences and to the mathematics profession.”

A description of the Fellows program is at

Founded in 1888 to further mathematical research and scholarship, the American Mathematical Society fulfills its mission through programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life.



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Fall 2017 Joseph Fels Ritt Lectures

Come join us Monday October 30th & Wednesday November 1st at 4:30 pm in RM 520, Professor László Székelyhidi Jr. (University of Leipzig) will be giving a special lecture about “The h-principle in fluid dynamics”.

Professor László Székelyhidi Jr. (University of Leipzig)


The h-principle in Fluid Dynamics


It is known since the pioneering work of V. Scheffer and A. Shnirelman in the 1990s that weak solutions of the incompressible Euler equations behave in very unexpected ways. Such solutions are highly non-unique and have several unphysical features such as arbitrary growth of energy. Nevertheless, weak solutions in three space dimensions have been studied in connection with a conjecture of L. Onsager from 1949 concerning anomalous dissipation and, more generally, because of their possible relevance to Kolmogorovs K41 theory of turbulence.

In a series of joint publications with Camillo De Lellis we established a connection between the theory of weak solutions of the Euler equations and the Nash-Kuiper theorem on rough isometric immersions. Through this connection one can interpret the wild behavior of weak solutions of the Euler equations as an instance of Gromov’s celebrated h-principle. In these lectures I will explain this connection, outline the most recent progress concerning Onsager’s conjecture and discuss some future directions.

Time & Location

Monday October 30, 2017 & Wednesday November 1, 2017 at 4:30 pm

Mathematics Hall, Room 520

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Invidious Comparisons: International politics, the Fields Medal, and the past, present, and future of mathematics, 1936-1966


Invidious Comparisons: International Politics, the Fields Medal, and the Past, Present, and Future of Mathematics, 1936-1966 


First presented in 1936, the Fields Medal quickly became one of mathematicians’ most prestigious, famous, and in some cases notorious prizes. Because its deliberations are confidential, we know very little about the early Fields Medals: how winners were selected, who else was considered, what values and priorities were debated—all these have remained locked in hidden correspondence. Until now. This talk will analyze newly discovered letters from the 1950 and 1958 Fields Medal committees, which Dr. Barany claims demands a significant change to our understanding of the first three decades of medals. He will show, in particular, that the award was not considered a prize for the very best mathematicians, or even for the very best young mathematicians. Debates from those years also shed new light on how the age limit of 40 came about, and what consequences this had for the Medal and for the mathematics profession. ​This talk will argue that 1966 was the turning point that set the course for the Fields Medal’s more recent meaning.

This event is free and open to the public.
This event is part of the New York History of Science Lecture Series.


513 Fayerweather Hall, Columbia University
1180 Amsterdam Avenue, New York, NY 


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