Georgia Institute of Technology College of Sciences

Professor Henry Segerman presents the Frontiers in Science Public Lecture "3D Shadows: Casting Light on the Fourth Dimension", author of Visualizing Mathematics with 3D Printing

Book signing will follow the lecture.

Speaker: Henry Segerman
Affiliation: Department of Mathematics, Oklahoma State University
Host: Stavros Garoufalidis
When: Oct. 27, 2016, 7:30 pm
Where: Student Success Center - Clary Theatre

Abstract

Our brains have evolved in a three-dimensional environment, and so we are very good at visualizing two- and three-dimensional objects. But what about four-dimensional objects? The best we can really do is to look at three dimensional "shadows". Just as a shadow of a three-dimensional object squishes it into the two-dimensional plane, we can squish a four-dimensional shape into three-dimensional space, where we can then make a sculpture of it. If the four-dimensional object isn’t too complicated and we choose a good way to squish it, then we can get a very good sense of what it is like. We will explore the sphere in four-dimensional space, the four-dimensional polytopes (which are the four-dimensional versions of the three-dimensional polyhedra), and various 3D printed sculptures, puzzles, and virtual reality experiences that have come from thinking about these things.

Ravi Kannan from Microsoft Research India will present the ACO Distinghished Lecture on November 1, 2011 at 4:30 pm in Klaus 1116.

Ravindran (Ravi) Kannan is Principal Researcher in the Algorithms Research Group at Microsoft Research Bangalore. Previously he was a professor at CMU, MIT, and Yale, where he was the William Lanman Professor of Computer Science. His research areas span Algorithms, Optimization and Probability. He is widely known for introducing several groundbreaking techniques in theoretical computer science, notably in the algorithmic geometry of numbers, sampling and volume computation in high dimension, and algorithmic linear algebra. He received the Knuth Prize in 2011, and the Fulkerson Prize in 1992. He is a distinguished alumnus of IIT Bombay.

Vectors, Sampling and Massive Data

Modeling data as high-dimensional (feature) vectors is a staple in Computer Science, its use in ranking web pages reminding us again of its effectiveness. Algorithms from Linear Algebra (LA) provide a crucial toolkit. But, for modern problems with massive data, these algorithms may take too long. Random sampling to reduce the size suggests itself. I will give a from-first-principles description of the LA connection, then discuss sampling techniques developed over the last decade for vectors, matrices and graphs. Besides saving time, sampling leads to sparsification and compression of data.

There will be a reception in the Atrium of the Klaus building at 4PM.

The Southeast Geometry Seminar is a series of semiannual one-day events focusing on geometric analysis. These events are hosted in rotation by the following institutions:

• The University of Alabama at Birmingham 
• The Georgia Institute of Technology
• Emory University 
• The University of Tennessee Knoxville 

The following five speakers will give presentations on topics that include geometric analysis, and related fields, such as partial differential equations, general relativity, and geometric topology.

• Jason Cantarella (University of Georgia)
• Meredith Casey (The Georga Institute of Technology)  
• Kirk Lancaster (Wichita State University)
• Junfang Li ( University of Alabama at Birmingham)  
• Jason Parsley (Wake Forest University)

The general public lecture will be presented by Jason Cantarella (University of Georgia) entitled The Square Peg Theorems or What does it mean to solve simultaneous equations? to take place in Klaus 1116 at 5:00PM

Gil Kalai from the Hebrew University of Jerusalem will present the Algorithms, Combinatorics and Optimization (ACO) Distinguished Lecture on September 13, 2012 at 4:30 pm in Weber Space Science and Technology Building II (Weber SST II) Room 2.

There will be a reception in the lobby of Weber SST II at 4 p.m.

Gil Kalai, is the Henry and Manya Noskwith Professor of Mathematics at the Hebrew University of Jerusalem. He has a long term visiting position at Yale University and he is a frequent visitor to Microsoft Research.

Kalai's main research areas are combinatorics and convexity. He is interested in the combinatorial theory of convex polytopes, relations of combinatorics with topology and with Fourier analysis, Boolean functions, and threshold and isoperimetric phenomena. His interests also include applications to and connection with theoretical computer science, mathematical programming, probability theory, quantum computing, and game theory.

Kalai is the recipient of the 1992 Polya Prize, the 1993 Erdös Prize, the 1994 Fulkerson Prize and the 2012 Rothschild Prize. He is a member of the Center for the Study of Rationality as well as the Center for Quantum Information Science at the Hebrew University. He has served in several scientific committees at the university as well as at the national and international levels and he belongs to several editorial boards. In the last years he has been writing a scientific blog, Combinatorics and More, and has been active in various Internet mathematical activities.

Analysis of Boolean Functions, Influence and Noise

A few results and two general conjectures regarding analysis of Boolean functions, influence, and threshold phenomena will be presented.

• Boolean functions are functions of n Boolean variables with values in {0,1}. They are important in combinatorics, theoretical computer science, probability theory and game theory.
• Influence: Causality is a topic of great interest everywhere, and if causality is not complicated enough, we can ask what is the influence one event has on another one. In a 1985 paper, Ben-Or and Linial, studied influence in the context of collective coin flipping -- a problem in theoretical computer science.
• Fourier analysis: Over the last two decades, Fourier analysis of Boolean functions and related objects played a growing role in discrete mathematics and theoretical computer science.
• Threshold phenomena: Threshold phenomena refer to sharp transition in the probability of certain events depending on a parameter p near a critical value. A classic example that goes back to Erdös and Rényi, is the behavior of certain monotone properties of random graphs.

Influence of variables on Boolean functions is connected to their Fourier analysis and threshold behavior as well as to discrete isoperimetry and noise sensitivity.

The first conjecture to be described (with Friedgut) is called the Entropy-Influence Conjecture (it was featured on Tao's blog). It gives a far reaching extension to the KKL theorem, and theorems by Friedgut, Bourgain, and me.

The second conjecture (with Kahn) proposes a far-reaching generalization to results by Friedgut, Bourgain and Hatami.

References

1. J. Bourgain and G. Kalai, Influences of variables and threshold intervals under group symmetries GAFA 7 (1997), 438-461.
2. H. Hatami, A structure theorem for Boolean functions with small total influences, Ann. of Math., to appear.
3. J. Kahn and G. Kalai, Thresholds and expectation thresholds, Comb., Prob. and Comp., 16 (2007), 495-502.

GT MAP sponsored "Workshop on Dynamical Systems" to mark the retirement of Prof. Shui Nee Chow.

After nearly 30 years at Georgia Tech, Prof. Shui Nee Chow has officially retired.  This workshop will see several of his former students, post-docs, and friends, coming together to thank Shui Nee for his vision, service, and research, that so greatly impacted the School of Mathematics at Georgia Tech.

The workshop will be held in the Klaus building Room 1447.  Poster can be found HERE.

View PHOTOS from the event.

Tentative Schedule and  PROGRAM  >

Thursday August 10

 8:30-  9:00   Coffee

 9:00-  9:10    Welcome by COS Dean Paul Goldbart

 9:10-  9:50   Erik Van Vleck (Kansas) on "Projected Data Assimilation and Applications"

 9:50- 10:30   Wenzhang Huang (Alabama in Huntsville) on "Global dynamics of a ratio-dependent Holling-Tanner Predator-prey system"

10:30-11:00   Coffee

11:00-11:25    Wuchen Li (UCLA) on "Dynamical system on finite graphs"

11:25-12:05   Wenxian Shen (Auburn) on "Transition Fronts in Nonlocal Dispersal Evolution Equations"

12:05- 1:30    Lunch

 1:30- 2:10   John Mallet-Paret (Brown) on "Some Generic Properties of Delay-Differential Equations"

 2:10- 2:35   Sung Ha Kang (GT Math) on "Path optimization for surveillance"

 2:35- 3:00   Chongchun Zeng (GT Math) on "Instability, index theorems, and exponential dichotomy of Hamiltonian PDEs"

 3:00- 3:30   Coffee

 3:30- 4:10   Eric Carlen (Rutgers) on "Operator inequalities, Non-commutative Probability and Quantum Statistical Mechanics"

 4:10- 4:35   Conceicao (Sao) Carvalho (Lisboa, Portugal) on "Quantum Master Equations in Kinetic Theory"

 4:35- 5:00   Rafael de la llave (GT Math) on "Manifolds on the verge of a hyperbolicity breakdown"

Friday August 11

 8:30-  9:00   Coffee

 9:00-  9:40   Konstantin Mischaikow (Rutgers) on "How to rigorously solve \dot{x} =? "

 9:40-10:20  Weishi Liu (Kansas) on "Analysis of ion channel problems"

10:20-10:45 Rachel Kuske (GT Math) on "Stochastic averaging for multiple scale models driven by fat-tailed noise"

10:45-11:15  Coffee

11:15-11:55  Todd Young (Ohio) on "Dynamics of Tensor Approximation in Narrow Valleys"

11:55-12:20  Cinzia Elia (Bari, Italy) on "On periodic orbits of discontinuous dynamical systems"

12:20- 2:00  Lunch

 2:00- 2:40   Bo Deng (Univ. of Nebraska-Lincoln) on "Conductance-resistance symmetrical model for neurons"

 2:40- 3:05   Howie Weiss (GT Math) on "Antibiotic Cycling: A cautionary tale"

 3:05- 3:30   Coffee

 3:30 - 4:10  Kening Lu (Brigham Young University) : SRB measure and Horseshoe for infinite dimensional dynamical systems.

 4:10- 4:35   Evans Harrell (GT Math) on "What does the average eigenvalue know?"

 4:35- 5:15   Jim Yorke (Maryland) on "What's the point ?"

We look forward to seeing you there.

The goal of this workshop is to bring together experts in various aspects of optimal transport and related topics on graphs (e.g., PDE/Numerics, Computational and Analytic/Probabilistic aspects).

The meeting will take place at Skiles 006.
Organizers: Shui-Nee Chow, Wilfrid Gangbo, Prasad Tetali, and Haomin Zhou

Click here for tentative schedule with title and abstract. 

Tuesday, May 9, 2017

10:05 – 10:55am : Stan Osher (UCLA)

11:05 – 11:55am : Max Fathi (CNRS, Lyon, France)

LUNCH

1:30 – 2:20pm : Paul-Marie Samson (U. of Paris-Est, Marne La Vallee)

Break

3:05 – 3:55pm : Wuchen Li (UCLA)

4:05 – 4:55pm : Xiaojing Ye (Georgia State University)
 

Wednesday, May 10, 2017

09:30 – 10:20am : Adam Oberman (McGill University)

10:30 – 11:20am : Nicolas Garcia Trillos (Brown University)

11:30 – 12:20pm : Michael Loss (Georgia Tech)

LUNCH

1:30 – 2:20pm :  Paul Horn (University of Denver)

2:30 - 3:20PM :  J.D. Walsh (Georgia Tech)

Prasad Tetali was one of two winners for the CoS Faculty Mentor award. This award recognizes the time and effort that faculty members spend in mentoring and expresses the Institute's appreciation for the mentor's services to the community. The award will be presented at the College of Sciences/ADVANCE reception on April 15, 4-5:30 pm in the Library's Ferst room.

This week, one of Georgia Tech's favorite calculus professors, Tom Morley will be the featured guest on the WREK talk show called "Inside the Black Box." Morley will join hosts Pete Ludovice and Bill Hunt to talk about calculus in a segment entitled "Calculus: Math in Motion". The discussion won't just cover why calculus impresses people at cocktail parties, but actually what it is and how it is useful. Tune in Wednesday September 8, 2009 from noon to 1:00 pm EDT to WREK 91.1 FM or listen online at http://www.wrek.org/blackbox.

Prospective Student Day

Students interested in graduate studies in the School of Mathematics are invited to attend Prospective Student Day on * Friday November 2, 2012 *

This will be an afternoon event, and light refreshments will be served. You are welcome to visit our school, hear about graduate degree options available in the School of Mathematics, learn about requirements for admission, as well as meet our faculty and current graduate students. Prospective students from underrepresented groups in the mathematical sciences and students from the Atlanta area are particularly encouraged to attend.

If you plan to come, please let us know by emailing your name, the year you plan to graduate and the college you are attending to the graduate coordinator. We will follow up with details.

Schedule of events:

Time         Activity

2:00-2:45   Welcome/Presentation by Graduate Director

2:45-3:00   Break

3:00-3:45   Panel Discussion with Current Graduate Students

3:45-4:30   Tea with Faculty and Current Graduate Students

4:30-5:30   Department and Campus Tour

Previous post before the conference:

Federico Bonetto, Evans Harrell, and Michael Loss are hosting the conference series "Mathematical Results in Quantum Theory" (or QMath). The series was initiated by P. Exner and P. Seba in 1987. The aim is not only to bring together people interested in the "quantum part" of mathematical physics, but also to stimulate a search of new quantum effects and a deeper understanding of quantum physics, as well as the development of methods which can help in situations where the standard quantum mechanical tools are inadequate. Up to now there have been twelve meetings, the thirteenth is to be held at the Georgia Institute of Technology during October 8-11, 2016.

Post after the conference: