December 13, 2018 | Atlanta, GA

Arkadi Nemirovski has been awarded the 2019 Norbert Wiener Prize in Applied Mathematics. The prize is awarded once every 3 years by AMS and SIAM for an outstanding contribution to applied mathematics in the highest and broadest sense. The citation reads:

The 2019 Norbert Wiener Prize in Applied Mathematics will be awarded to Professor Arkadi Nemirovski for his fundamental contributions to high-dimensional optimization and for his discovery of key phenomena in the theory of signal estimation and recovery.

A powerful and original developer of the mathematics of high-dimensional optimization, Nemirovski, with D. Yudin, invented the ellipsoid method used by Leonid Khachiyan to show for the first time that linear programs can be solved in polynomial time. With Yurii Nesterov, he extended interior‐point methods in the style of Narendra Karmarkar to general nonlinear convex optimization. This foundational work established that a rich class of convex problems called semidefinite programs are solvable in polynomial time. Semidefinite programs are now routinely used to model concrete applied problems and to study deep problems in theoretical computational complexity. A third breakthrough, with Aharon Ben-Tal, was the invention of methods of robust optimization to address problems in which the solution may be very sensitive to problem data. Nemirovski also and rather amazingly made seminal contributions in mathematical statistics, establishing the optimal rates at which certain
classes of nonparametric signals can be recovered from noisy data and investigating limits of performance for estimation of nonlinear functionals from noisy measurement. His contributions have become bedrock standards with tremendous theoretical and practical impact on the field of continuous optimization and beyond.

Find out more about the Wiener Prize and see previous recipients here.

This story originally appeared on the ACO gatech webpage

December 3, 2018 | Atlanta, GA

The Georgia Tech Algorithms, Combinatorics, and Optimization Program (ACO) has selected Chun-Hung Liu to receive the 2018 ACO Outstanding Student Prize. The award recognizes academic excellence in the areas represented by ACO.

Liu’s selection is based on two major accomplishments. First, he did breakthrough research as a Ph.D. student by resolving the Robertson conjecture for topological minors, namely that graphs that do not have a Robertson chain of fixed length as a topological minor are well-quasi-ordered.

Second, Liu developed and refined parts of the classical Robertson-Seymour theory, discovering entirely new methods alongside. In addition, he is honored for displaying an exemplary attitude toward research and scholarship.

Liu received B.S. and M.S. degrees in mathematics from the National Taiwan University, in Taiwan. After completing the Georgia Tech Ph.D. program in Algorithms, Combinatorics, and Optimization in 2014, he joined Princeton University as an instructor. In 2018, he moved to Texas A&M University as an assistant professor of mathematics.

“I am very grateful to Prof. Thomas for his constant support and encouragement during my life at Georgia Tech. His professionalism, passion, and leadership undoubtedly shaped my development.”

School of Mathematics Professor Robin Thomas was Liu’s supervisor at Georgia Tech. Thomas recalls Liu as “a very strong student,” passing the comprehensive examination early and then writing four strong papers in quick succession. This achievement earned Liu the school’s Top Graduate Student Award while only in his second year.  “I expect he will become a regular invitee to Graph Theory meetings in Oberwolfach, Banff, and elsewhere,” Thomas says.

Liu says he “deeply benefited” from ACO, which he describes as a “wonderful multidisciplinary program that integrates three fascinating and active directions in an amazingly terrific way.”

Liu adds: “I am very grateful to Prof. Thomas for his constant support and encouragement during my life at Georgia Tech. His professionalism, passion, and leadership undoubtedly shaped my development.”

December 3, 2018 | Atlanta, GA

The Georgia Tech Algorithms, Combinatorics, and Optimization Program (ACO) has selected Chun-Hung Liu to receive the 2018 ACO Outstanding Student Prize. The award recognizes academic excellence in the areas represented by ACO.

Liu’s selection is based on two major accomplishments. First, he did breakthrough research as a Ph.D. student by resolving the Robertson conjecture for topological minors, namely that graphs that do not have a Robertson chain of fixed length as a topological minor are well-quasi-ordered.

Second, Liu developed and refined parts of the classical Robertson-Seymour theory, discovering entirely new methods alongside. In addition, he is honored for displaying an exemplary attitude toward research and scholarship.

Liu received B.S. and M.S. degrees in mathematics from the National Taiwan University, in Taiwan. After completing the Georgia Tech Ph.D. program in Algorithms, Combinatorics, and Optimization in 2014, he joined Princeton University as an instructor. In 2018, he moved to Texas A&M University as an assistant professor of mathematics.

“I am very grateful to Prof. Thomas for his constant support and encouragement during my life at Georgia Tech. His professionalism, passion, and leadership undoubtedly shaped my development.”

School of Mathematics Professor Robin Thomas was Liu’s supervisor at Georgia Tech. Thomas recalls Liu as “a very strong student,” passing the comprehensive examination early and then writing four strong papers in quick succession. This achievement earned Liu the school’s Top Graduate Student Award while only in his second year.  “I expect he will become a regular invitee to Graph Theory meetings in Oberwolfach, Banff, and elsewhere,” Thomas says.

Liu says he “deeply benefited” from ACO, which he describes as a “wonderful multidisciplinary program that integrates three fascinating and active directions in an amazingly terrific way.”

Liu adds: “I am very grateful to Prof. Thomas for his constant support and encouragement during my life at Georgia Tech. His professionalism, passion, and leadership undoubtedly shaped my development.”

December 12, 2018 | Atlanta, GA

While in high school, Bharath Hebbe Madhusudhana wanted to be a mathematician or a physicist. Now, he takes home degrees in the two fields he esteems the most: an M.S. in Mathematics and a Ph.D. in Physics.

The mathematics degree was almost an afterthought. When Bharath began his Ph.D. program in physics, he also started taking one graduate-level class in mathematics per semester. Before long, he needed only a few more, as well as a thesis, to complete the requirements of the master’s degree.

Prior to Tech, Bharath completed his undergraduate degree in physics in the Indian Institute of Technology (IIT) Kanpur, in Uttar Pradesh, India. He knew he would do a Ph.D. “I joined Georgia Tech in the pursuit of a place where cutting-edge research was being done,” he says.

At Tech, Bharath not only studied his major fields but also pushed himself to communicate his science well. In 2016, he participated in Georgia Tech’s Three Minute Thesis Competition. Competitors explained their research to a diverse audience in just three minutes.

At the time, Bharath was a fourth-year Ph.D. student. He had discovered something fundamental about rubidium atoms: When cooled to about 170 nanoKelvins – almost absolute zero – and exposed to a magnet that traces a circle around them, the very-low-energy rubidium atoms can remember something abstract. They can tell the area of an abstract surface – called the Boy’s surface – corresponding to the real traced circle.

For his spirited explanation of how atoms, when cooled to almost immobility, remember abstract geometric phenomena, the judges named Bharath the third-place winner and the audience voted him as one of two winners of the People’s Choice award.

What is the most important thing you learned at Georgia Tech?
Apart from the technical knowledge necessary to conduct scientific research in my area, I learned the art of academic communication and collaboration in research. The papers I wrote and the conferences I attended helped me learn the basics of communicating my research work. While working with multiple faculty members at Georgia Tech, I gained experience in scientific collaboration.  

What is your proudest achievement at Georgia Tech?
One of my research papers was rejected three times in a row by the same journal. However, with a carefully crafted rebuttal, I got it published after the fourth resubmission. The process was challenging, but I was supported extensively by the faculty members at Georgia Tech. 

Which professor(s) or class(es) made a big impact on you?
I gained a lot from the technical guidance of my advisor, Professor Michael Chapman. I owe my experimental skills and my intuitive understanding of atomic physics to him. He also provided valuable advice on crucial career-related decisions that I had to make in the later part of my Ph.D. work. His guidance has been pivotal in my professional development.

Professors Brian Kennedy and Carlos Sa de Melo also made a significant impact on my understanding of physics.

Professor Kennedy was always welcoming and available to talk about the theoretical aspects of our experiment. The discussions he had with me helped steer my research work into a productive direction. He also helped me extensively in writing a theoretical research paper and getting it published. During this process, with Professor Kennedy’s support, I learned how to respond to critical reviews of a research paper.

Being an experimental atomic physicist, I owe almost all my understanding of condensed-matter theory to Professor Sa de Melo. He is very friendly and always enthusiastic to talk about physics. I remember several late-night discussions with him in the laboratory, which resulted in a research paper that he and I wrote.  

I am grateful to two professors from the School of Mathematics, Greg Blekherman and John Etnyre.

As my master’s thesis advisor, Professor Blekherman is responsible for my technical knowledge in the area of convex optimization.  He was kind and accommodating as a thesis supervisor.

Professor Etnyre helped me understand the mathematical basis of my thesis project, which involved the fascinating subject of topology. He was always made himself available for discussions, from which I benefited greatly.   

What is your most vivid memory of Georgia Tech?
I have several.

Professor Sa de Melo would sometimes come to our lab at 9 PM. Along with a freshly brewed pot of tea, we talked about physics. Sometimes, we would lose track of time, only to realize that it is past 1 AM and we should call it a day. These discussions alone have resulted in a couple of research papers.

In the evenings, I would go on long walks, circling the campus area, occasionally stopping at the Campus Recreation Center for a swim or rock climbing or a game of ping-pong.

In what ways did your time at Georgia Tech transform your life?
Professionally, I now have a clear view of what I am going to do. At Georgia Tech, along with the acquiring the necessary technical skills, I developed an understanding of the goals of the specific research field. This understanding helped me decide what I want to do next.  

What unique learning activities did you undertake?
In 2016, Professor Chapman encouraged me to participate in the Three Minute Thesis (3MT) Competition at Tech. The challenge was to communicate my thesis work in three minutes to a nonexpert audience.

While preparing for 3MT, I learned the art of oral communication, and it changed the way I presented my work at conferences thereafter. I was fortunate to win prize money, which I used to attend a conference. Professor Chapman had the foresight to know that participating in 3MT would be a good step in my professional development.

What advice would you give to incoming graduate students at Georgia Tech? Georgia Tech has vast intellectual wealth, held by the numerous knowledgeable faculties in various disciplines. I would advise incoming graduate students to make use of this resource, as well as the facilities available on campus, to maximize their intellectual development during their time here.

Where are you headed after graduation?
I am starting a postdoctoral position at the Max Planck Institute of Quantum Optics, in Garching, Germany.

Professors Chapman, Kennedy, and Sa de Melo helped me develop the skills and confidence to continue in academia.They prepared me for an academic career, particularly for this postdoctoral position.

Wenlei Li

Contact Information

Welcome  This is the eighth annual Tech Topology Conference. It brings together established and beginning researchers from around the country for a weekend of mathematics in Atlanta. Check back soon for more details. We are pleased to announce this year's speakers: 

The 2018 conference features several session of five-minute lightning talks. 

If you are interested in giving such a talk (on behalf of your work or someone else’s) please see the "Registration and Support" page. 
Deadline for submitting proposals for Lightning Talks is October 31.

website: http://people.math.gatech.edu/~etnyre/TechTopology/2018/index.html

organizers: J. Etnyre, J. Hom, K. Kordek, P. Lambert-Cole, C. Leverson, D. Margalit, J. Park, and B. Strenner
Supported by the NSF and the Georgia Institute of Technology

Event Details

Date/Time:

Qinbo Chen

Contact Information

November 7, 2018 | Atlanta, GA

Volume X Contents

  • Welcome from the Chair
  • Benefits Add Up for Undergrads in SoM REU Programs
  • Seven REUs Planned for Summer 2018
  • Georgia Tech Hosts Annual High School Competition
  • Libby Taylor Feature: Georgia Tech Undergrad Takes Home AWM Math Prize
  • Annual TA Student Award Winners
  • Recent Graduates Give Advice to Incoming Freshmen
  • Geometric Group Theory Gets an Informal Take from Tech Professor
  • Donor Awards
  • PhD Program
  • Events
  • Awards
  • Featured Article: Researchers Determine Routes of Respiratory Infection Disease Transmission on Aircraft
  • Members of SoM at the Helm of National Research Programs
  • Discrete Math/Combinatorics Moves Up to No. 2 in US News Graduate School Rankings
  • Faculty Profiles
  • Teaser: New Frontiers Beckon Math and Biology in Multi-million Dollar NSF-Simons Project
  • ProofReader Article Picked Up by Notices of American Math Society
  • SoM Professor Called to Give Expert Testimony in Jury Selection Case

Please see the Proofreader page on our website or click here to view a .pdf of the new ProofReader. 

Please send comments to Sal Barone at comm@math.gatech.edu, with subject line "ProofReader".

November 7, 2018 | Atlanta, GA

Volume X Contents

  • Welcome from the Chair
  • Benefits Add Up for Undergrads in SoM REU Programs
  • Seven REUs Planned for Summer 2018
  • Georgia Tech Hosts Annual High School Competition
  • Libby Taylor Feature: Georgia Tech Undergrad Takes Home AWM Math Prize
  • Annual TA Student Award Winners
  • Recent Graduates Give Advice to Incoming Freshmen
  • Geometric Group Theory Gets an Informal Take from Tech Professor
  • Donor Awards
  • PhD Program
  • Events
  • Awards
  • Featured Article: Researchers Determine Routes of Respiratory Infection Disease Transmission on Aircraft
  • Members of SoM at the Helm of National Research Programs
  • Discrete Math/Combinatorics Moves Up to No. 2 in US News Graduate School Rankings
  • Faculty Profiles
  • Teaser: New Frontiers Beckon Math and Biology in Multi-million Dollar NSF-Simons Project
  • ProofReader Article Picked Up by Notices of American Math Society
  • SoM Professor Called to Give Expert Testimony in Jury Selection Case

Please see the Proofreader page on our website or click here to view a .pdf of the new ProofReader. 

Please send comments to Sal Barone at comm@math.gatech.edu, with subject line "ProofReader".

November 7, 2018 | Atlanta, GA

Mysteries of Floating

-By John McCuan

We are used to seeing a light object, like a beach ball, float on the surface of water while a heavy one, like a solid silver ball, sinks to the bottom (Fig.1-Fig.2). Over two-thousand years ago, based on similar observations, Archimedes proposed a simple and beautiful rule to determine which objects float, which objects sink, and how much liquid will be displaced by a floating object. He asserted that everything should be determined by relative densities.

Archimedes might be surprised to see this green plastic ball (Fig. 3-Fig. 5) which sinks to the bottom if pushed below the surface but also floats on the surface of the water if it is gently released there. The framework needed to understand the behavior of a “heavy” floating ball like this one was introduced by the mathematician Carl Friedrich Gauss in 1830. He applied his ideas about minimizing energy to the geometrical and analytical concepts of surface tension and contact angle introduced by Thomas Young and Pierre Simone Laplace in 1805 and 1806.

Nevertheless, theoretical verification of the possibility of a heavy floating object like the green ball was first obtained by Rajat Bhatnagar and Robert Finn of Stanford University in 2006. To obtain their result various simplifications were made. One of those simplifications was to assume the liquid bath was infinite in extent with the walls of the container infinitely far away. John McCuan of the School of Mathematics has been interested in floating objects in laterally bounded containers since about the same time. In 2013 he was able, along with Ray Treinen of Texas State University, to analyze the energy landscape for problems that include the green ball floating in a finite cylindrical container as in the photo above. They showed, in particular, that if such a ball, floating on the surface of the water is pushed downward, the energy of the system will increase at first, eventually reaching a single maximum, at which point, as the ball moves lower, the energy of the system decreases and eventually the ball slips below the surface and sinks.

While relaxing the assumption of an infinite sea on which the ball floats, McCuan and Treinen introduced an additional symmetry assumption, effectively requiring the ball to be constrained to a frictionless vertical wire through its center keeping the ball in the middle of a circular cylindrical container. The characterization of parameters (density, surface tension versus gravity, the size of the ball relative to that of the container, and adhesion properties) for which a floating ball will remain in the center without the guide-wire is still a major open problem.

Buoyed up by some success, McCuan and Treinen attempted to characterize the equilibrium configurations (maxima and minima of the Gauss energy) for balls like the beach ball with density lower than that of the liquid. They were able to obtain a number of results, but they were also in for a big surprise. The natural expectation would be that for the light ball there is a unique equilibrium (energy minimum) with the energy increasing monotonically as the ball is pushed downward (and constrained to the center) in a cylindrical container. This is true for a beach ball in, say, a swimming pool. Sometimes, however, for certain collections of parameters, the energy will, in fact, increase but then decrease to another local minimum before increasing as the ball is submerged. (See chart, first image)

Note: For purposes of illustration the figure is neither to scale nor accurately proportioned.

There are several consequences of this 2018 discovery. One is that a ball floating in a cylinder need not have a unique floating height; the ball may rest at equilibrium in two different positions. If, for example, the ball is positioned as on the left, it will remain there, but if the ball is manually moved to the position on the right, it will also float in position there. Such a ball in a cylinder might be used as a two position switch. Furthermore, the phenomenon first encountered with the heavy green ball is not isolated to the heavy floating ball. Even with a light floating ball, the observed floating configuration can depend on where one positions the ball initially. The only known instances of this behavior for a light ball occur when the ball fits within the cylinder leaving only a small gap (several one hundredths of a millimeter) between the ball and the wall, so the phenomenon would likely never have been discovered without considering the case of laterally bounded containers.

Other “fun” facts:

  • 1. It was about 200 years between the time a mathematical framework describing floating objects (including capillarity and adhesion energies) was proposed and the time it was actually used with any success to describe floating objects.

Part of the groundwork for this kind of application of the theory was laid in McCuan’s 2007 paper which adapts the framework of Gauss to situations which allow floating. Previous to this, force phenomena such as buoyancy were viewed as separate from capillary equilibrium theory. McCuan showed all conditions for equilibrium (including various generalized force equations) follow from the basic approach of Gauss.

  • 2. An essential difference between the analysis of floating objects (say balls) based on Archimedes’ principle and that based on capillarity is that in the former the liquid surface is assumed to be a flat plane, while in the latter the geometric shape of the liquid surface can be curved and plays a central role. Sometimes the liquid surface surrounding a floating ball can be so far from a plane that it bends back over itself as suggested by the exaggerated figure below.[PP] Several results in the paper of McCuan and Treinen (2013) give conditions under which this cannot happen. They show, for example, that if the ball is too heavy (dense) or the ball is too small, then such “folding over” is not possible. Also, if the ball is too light and the adhesion of the liquid with the ball is too small (resulting in an angle between the liquid and the ball measured within the liquid which is too big), then, again, folding over is not possible.
  • 3. Another factor in the recent progress on problems like this (in spite of interest in them from antiquity) is the new capability to numerically analyze the model equations.
  • 4. One approach (and perhaps the only approach) to understanding when a floating ball will remain centered in the container (rather than move to the side) requires an extension of McCuan’s 2007 first variation formula to the second variation of energy. In some instances (experimentally) when the outer edge of the liquid interface is higher than the edge on the ball, and the ball is heavy, the ball will stay in the center. Similarly, when the outer edge is lower than the inner edge, then a heavy ball will tend to the side. These observations can be reversed for a light ball. These experimentally observed conditions are (first of all) far from a mathematical analysis; it is very unlikely that they capture the entire range of possibilities.
  • 5. Most of the known results are for a system which is simplified in dimension. Mathematically, we are really considering (in the drawings above for example) a two dimensional problem which can be viewed as treating an infinite log (extending directly out of the paper) floating in a trough. It seems likely that all equilibria for this simplified problem can be identified/classified within the next decade. A similar time frame applies to the spherical ball in a cylindrical container as indicated in the photographs. Some fundamental advance, like obtaining a second variational formula for energy as mentioned in the previous point will be necessary for understanding/classifying the conditions characterizing central floating versus moving to the side.

References:

250 B.C. Archimedes, On floating bodies

1805 Thomas Young, An essay on the cohesion of fluids, Philos. Trans. R. Soc. Lond. 95[PP]

1806 Pierre Simone Laplace, Mécanique céleste

2006 Raj Bhatnagar and Robert Finn, Equilibrium configurations of an infinite cylinder in an unbounded fluid. Phys. Fluids 18 no. 4

2007 John McCuan, A variational formula for floating bodies, Pac. J. Math. 231 no. 1

2009 John McCuan, Archimedes’ principle revisited, Milan J. Math. 77

2013 John McCuan and Ray Treinen, Capillarity and Archimedes’ principle of flotation, Pacific J. Math. 265 no 1

2018 John McCuan and Ray Treinen, On floating equilibria in a laterally finite container, SIAM J. Appl. Math. 78 no. 1

Pages

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