# Number theory

Thursday, August 24, 2017 - 9:00am - 9:45am

Kiran Kedlaya (University of California, San Diego)

We give a survey of some of the ways that number theorists use Sage. Among the basic objects we will encounter are elliptic curves, modular forms, and L-functions (including zeta functions).

Thursday, November 20, 2008 - 10:30am - 11:15am

Shmuel Onn (Technion-Israel Institute of Technology)

We develop an algorithmic theory of nonlinear optimization over sets

of integer points presented by inequalities or by oracles. Using a

combination of geometric and algebraic methods, involving zonotopes,

Graver bases, multivariate polynomials and Frobenius numbers, we provide

polynomial-time algorithms for broad classes of nonlinear combinatorial

optimization problems and integer programs in variable dimension.

I will overview this work, joint with many colleagues over the last few

of integer points presented by inequalities or by oracles. Using a

combination of geometric and algebraic methods, involving zonotopes,

Graver bases, multivariate polynomials and Frobenius numbers, we provide

polynomial-time algorithms for broad classes of nonlinear combinatorial

optimization problems and integer programs in variable dimension.

I will overview this work, joint with many colleagues over the last few

Wednesday, September 20, 2006 - 10:50am - 11:40am

J. Maurice Rojas (Texas A & M University)

One of the most basic notions in polynomial system

solving

is feasibility: does your system of equations have any roots?

We will

explore the algorithmic complexity of this problem, focussing

on

sparse polynomial systems over the real numbers and complex

numbers.

Over the complex numbers, we will see algorithms

completely

different from homotopy, resultants, and Grobner bases; and how

the

Generalized Riemann Hypothesis enters our setting. In

particular, we

solving

is feasibility: does your system of equations have any roots?

We will

explore the algorithmic complexity of this problem, focussing

on

sparse polynomial systems over the real numbers and complex

numbers.

Over the complex numbers, we will see algorithms

completely

different from homotopy, resultants, and Grobner bases; and how

the

Generalized Riemann Hypothesis enters our setting. In

particular, we

Thursday, October 2, 2014 - 9:00am - 9:50am

Boris Bukh (Carnegie-Mellon University)

Given a set of t words made of 0's and 1's, we wish to find a pair of them with a long common subsequence. How long a subsequence can be guarantee? It turns out that this question naturally leads to a decomposition of words into pieces that oscillate at approximately the same frequency. I will explain the solution to the problem above, and to some of the related questions. Based on the the joint works with J. Ma and L. Zhou.