First and Second Year Student Seminar

from Monday
January 01, 2018 to Thursday
May 31, 2018
Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars

Tuesday
January 30, 2018

5:30 PM - 6:30 PM
Math Tower 5-127
Jason Starr, Stony Brook University
Geometry and Topology and Arithmetic

Serge Lang had a saying, "Geometry determines Arithmetic." For instance, hyperbolic projective curves (of negative curvature) defined over global fields have at most finitely many "rational points" with coordinates in that global field (Faltings). Although elliptic curves (of zero curvature) can have infinitely many rational points, there are too few rational points to "approximate local points". Finally, rational curves (of positive curvature) with at least one rational point have enough rational points to approximate local points to all orders.

I will explain connections between geometry and arithmetic, I will explain the crucial role of topology, and I will explain theorems proving existence / approximation theorems for rational points using "higher positive curvature".


Tuesday
February 06, 2018

5:30 PM - 6:30 PM
Math Tower 5-127

No meeting


Tuesday
February 13, 2018

5:30 PM - 6:30 PM
Math Tower 5-127
Eric Bedford, Stony Brook University
Dynamics in Complex Dimension 2

We will discuss the following questions:

What are the manifolds in complex dimension 2 which carry nontrivial automorphisms? And how do you study the dynamics of these automorphisms?


Tuesday
February 27, 2018

5:30 PM - 6:30 PM
Math Tower 5-127
David Ebin, Stony Brook University
Motions with Strong Constraining Force

Professor Ebin will introduce us with some research topics in Motion of fluid and differential equations.


Tuesday
March 20, 2018

5:30 PM - 6:30 PM
Math Tower 5-127
Dennis Sullivan, Stony Brook University
A characterization of the smooth five manifold SU(3)/SO(3)

It is closed, simply connected , has dimension 4k+1 for some k and the homology is the smallest possible beyond that of the sphere of the same dimension, namely one Z/2Z in one intermediate degree.


Tuesday
April 03, 2018

5:30 PM - 6:30 PM
Math Tower 5-127
Moira Chas, Stony Brook University
Computer driven questions, pre-theorems and theorems in geometry

Several numbers can be associated to a free homotopy class X of closed curves on a surface S with negative Euler characteristic. Among these,
- the self-intersection number of X
- the word length of X
- the length of the geodesic corresponding to X [given a -1 curvature metric]
- the number of free homotopy classes of a given word length in the mapping class group orbit of X.

The interrelations of these numbers exhibit many patterns when explicitly determined or approximated by running a variety of algorithms on a computer.

We will discuss how these computations lead to counterexamples to existing conjectures and to the discovery of new patterns . Some of these new patterns, are so intricate and unlikely that they are certainly true (even if not proven yet), so they become "pre-theorems". Many of these pre-theorems later became theorems. An example of such a theorem states that the distribution of the self-intersection of free homotopy classes of closed curves on a surface, appropriately normalized, sampling among given word length, approaches a Gaussian when the word length goes to infinity. An example of a counterexample (no pun untended!) is that there exists pairs of length equivalent free homotopy classes of curves on a surface S that have different self-intersection number. (Two free homotopy classes X and Y are length equivalent if for every hyperbolic metric M on S, length(X)=length(Y).


Tuesday
April 10, 2018

5:30 PM - 6:30 PM
Math Tower 5-127
Ljudmila Kamenova, Stony Brook University
Hyperkaehler Geometry

Compact complex manifolds with vanishing first Chern class are built of irreducible blocks that are complex tori, Calabi-Yau manifolds and hyperkaehler manifolds. Hyperkaehler manifolds are simply connected and admit a non-degenerate holomorphic 2-form. Some basic problems in this area include coming up with more examples, classifying hyperkaehler manifolds in low dimensions and proving finiteness of their deformation types. For example, the only complex hyperkaehler surfaces are K3 surfaces, and they are all deformation equivalent to each other. Hyperkaehler geometry is still a relatively young field that started in the early 80's, and there are a lot of interesting directions and open problems. In this talk I will talk about several directions in hyperkaehler geometry.


Tuesday
April 17, 2018

5:30 PM - 6:30 PM
Math Tower 5-127
Leon Takhtajan, Stony Brook University
What is modern mathematical physics

The term “mathematical physics” is used in different senses and can have rather different content. This content changes with time, place and person.

By considering a few basic examples from different areas of mathematics I will explain my understanding of the subject.


Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars