Seminars and Colloquia by Series

Introduction to Sheaf Cohomology

Series
Other Talks
Time
Wednesday, September 30, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Matt Baker – School of Mathematics, Georgia Tech
After a few remarks to tie up some loose ends from last week's talk on locally ringed spaces, I will discuss exact sequences of sheaves and give some natural examples coming from real, complex, and algebraic geometry. In the context of these examples, we'll see that a surjective map of sheaves (meaning a morphism of sheaves which is surjective on the level of stalks) need not be surjective on global sections. This observation will be used to motivate the need for "sheaf cohomology" (which will be discussed in detail in subsequent talks).

Locally ringed spaces

Series
Other Talks
Time
Wednesday, September 23, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Matt Baker – School of Mathematics, Georgia Tech
I will discuss how various geometric categories (e.g. smooth manifolds, complex manifolds) can be be described in terms of locally ringed spaces. (A locally ringed space is a topological spaces endowed with a sheaf of rings whose stalks are local rings.) As an application of the notion of locally ringed space, I'll define what a scheme is.

Linear convergence of modified Frank-Wolfe algorithms for ellipsoid optimization algorithms

Series
Other Talks
Time
Tuesday, September 22, 2009 - 11:00 for 1 hour (actually 50 minutes)
Location
ISyE Executive Classroom, Main Building
Speaker
Michael J. Todd – School of Operations Research and Information Engineering, Cornell University
We discuss the convergence properties of first-order methods for two problems that arise in computational geometry and statistics: the minimum-volume enclosing ellipsoid problem and the minimum-area enclosing ellipsoidal cylinder problem for a set of m points in R^n. The algorithms are old but the analysis is new, and the methods are remarkably effective at solving large-scale problems to high accuracy.

Introduction to Sheaf Theory

Series
Other Talks
Time
Wednesday, September 16, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
John Etnyre – Ga Tech
In these talks we will introduced the basic definitions and examples of presheaves, sheaves and sheaf spaces. We will also explore various constructions and properties of these objects.

Math at Top Speed

Series
Other Talks
Time
Monday, September 14, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Student Services Building, Auditorium 117
Speaker
Richard Tapia – Rice University
In this talk Professor Tapia identifies elementary mathematical frameworks for the study of popular drag racing beliefs. In this manner some myths are validated while others are destroyed. Tapia will explain why dragster acceleration is greater than the acceleration due to gravity, an age old inconsistency. His "Fundamental Theorem of Drag Racing" will be presented. The first part of the talk will be a historical account of the development of drag racing and will include several lively videos.

Introduction to Sheaf Theory

Series
Other Talks
Time
Wednesday, September 9, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
John Etnyre – Ga Tech
In these talks we will introduced the basic definitions and examples of presheaves, sheaves and sheaf spaces. We will also explore various constructions and properties of these objects.

Introduction to Sheaf Theory

Series
Other Talks
Time
Wednesday, September 2, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
John Etnyre – Ga Tech
In these talks we will introduced the basic definitions and examples of presheaves, sheaves and sheaf spaces. We will also explore various constructions and properties of these objects.

Brown bag seminar on mathematical challenges in astrophysics

Series
Other Talks
Time
Wednesday, July 1, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Pablo Laguna – School of Physics, Georgia Tech
This will be an informal seminar with a discussion on some mathematical problems in relativistic astrophysics, and discuss plans for future joint seminars between the Schools of Mathematics and Physics.

On the sum-product problem

Series
Other Talks
Time
Monday, April 13, 2009 - 16:30 for 2 hours
Location
Skiles 269
Speaker
Jozsef Solymosi – Math, UBC
An old conjecture of Erdos and Szemeredi states that if A is a finite set of integers then the sum-set or the product-set should be large. The sum-set of A is A + A={a+b | a,b \in A\}, and the product set is defined in a similar way, A*A={ab | a,b \in A}. Erdos and Szemeredi conjectured that the sum-set or the product set is almost quadratic in |A|, i.e. max(|A+A|,|A*A|)> c|A|^{2-\epsilon}. In this talk we review some recent developments and problems related to the conjecture.

Twistor Theory, Then and Now

Series
Other Talks
Time
Wednesday, March 25, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Howey Physics Lecture Room 5
Speaker
Roger Penrose – Mathematical Institute, University of Oxford
Twistor theory is now over 45 years old. In December 1963, I proposed the initial ideas of this scheme, based on complex-number geometry, which presents an alternative perspective to that of standard 4-dimensional space-time, for the basic arena in which (quantum) physics takes place. Over the succeeding years, there were numerous intriguing developments. But many of these were primarily mathematical, and there was little interest expressed by the physics community. Things changed rather dramatically, in December 2003, when E. Witten produced a 99-page article initiating the subject of “twistor-string theory” this providing a novel approach to high-energy scattering processes. In this talk, I shall provide an account of the original geometrical and physical ideas, and also outline various recent developments, some of which may help our understandings of the seeming paradoxes of quantum mechanics.

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