## Iris Yoon

### Contact Information

**Title:** **Sparsity, oracles and inference in high-dimensional statistics**

**Thursday, September 6, 3:00pm-4:00pm, Skiles 006**

#### Event Details

**Date/Time:**

**Title:** **Sparsity, oracles and inference in high-dimensional statistics**

**Tuesday, September 4, 11:00am-12:00pm, Skiles 006**

#### Event Details

**Date/Time:**

**Title: TRIAD Distinguished Lecture Series by Sara van de Geer**

#### Event Details

**Date/Time:**

**Atlanta, GA**

A new national project, which includes the Georgia Institute of Technology, aims to convey the benefits of physics’ age-old intertwining with math upon biology, a science historically less connected with it. The National Science Foundation and the Simons Foundation have launched four centers to do this, funded with $40 million, one of which is headquartered at Georgia Tech and will receive a quarter of the funding.

Founding Members of the Organization include:

- Greg Bleckerman (GaTech SoM math)
- Christine Heitsch (GaTech SoM math)
- Natasha Jonoska (USF math)
- Julie Mitchell (UW-Madison math)
- Peter Bubenik (U. Florida math)
- Elena Dimitrova (Clemson math)
- Scott McKinley (Tulane math)
- Dan Goldman (GaTech physics)
- Francesca Storici (GaTech bio)
- Annalise Paaby (GaTech bio)
- Matt Torres (GaTech bio)
- Hang Lu (GaTech biochem)
- Melissa Kemp (GaTech bio-eng)
- Christine Payne (GaTech mech-eng)

*This article was edited from a story originally posted 5/24/2018 by Ben Brumfield. *

**Atlanta, GA**

Galina Livshyts, an assistant professor in the School of Mathematics, has received one of the highly competitive early-career grants from the National Science Foundation Faculty Early Career Development (CAREER) program.

NSF CAREER grants provide five years of funding to junior faculty. The award is a strong signal of recipients’ potential to serve as academic role models in research and education and to lead advances in the mission of their organization.

“My research is about geometry in two, three, and higher dimensions,” Livshyts says. The NSF CAREER grant enables her to explore the geometry of convex bodies in high dimensions.

A convex body is a geometric body having the property that any segment joining two of its points is entirely contained within it. Livshyts' research proposal aims to answer the following questions:

- What is the largest hyperplane section of a unit cube?
- How many translates of a slightly smaller copy of a convex body suffice to cover it?
- Can two different polygons have the same collection of normals and the same areas of triangles spanned by their sides?
- How large are the perimeters of convex sets with respect to isotropic log-concave measures?

“A lot of the geometric properties of convex bodies have important applications,” Livshyts says.

Suppose we have a million 10-inch-diameter ball-shaped items, and we need to pack them in an optimal way. What shape should we choose for the package? Some other questions in which the theory of convex bodies is used are directly related to the speed of certain algorithms.

NSF CAREER awards are unique in also requiring grant proposals to include an education component. Supporting junior researchers is the focus of Livshyts’ education component. During the term of the award, she will undertake several educational activities, including a research workshop for junior mathematicians, seminars for women in mathematics at all levels, and workshops for K-12 mathematics teachers.

“It is very important for a junior mathematician to be able to find just one other direction for their research, to create just one collaboration aside from their doctoral and postdoctoral work,” Livshyts says. She hopes her proposed five-day research workshop will give junior mathematicians – those in their final two years of their Ph.D. and those within five years after completing their Ph.D. – “an opportunity to expand their collaboration network and the circle of their interests early in their career.”

Livshysts has been organizing regular seminars for Women in Mathematics in Northern Georgia. In this activity she is joined by Yulia Babenko, an associate professor of mathematics at Kennesaw State University.

“Having a network of female researchers in Atlanta will bring more female participants to mathematics conferences,” Livshyts says. Mathematicians of all levels are invited to participate, and talks are intended for a general audience. “That will help junior participants expand their interests, as well as practice giving talks to a broad audience,” Livshyts says.

In spring 2018, Livshyts facilitated workshops at the Atlanta Intown Teachers’ Math Circles. Intended for K-12 mathematics teachers, the workshops will focus on nonstandard mathematics problems to increase participants’ mathematical knowledge and encourage creativity.

Livshyts is one of several School of Mathematics faculty members currently enjoying NSF CAREER grants.

“This award makes a great difference in my career,” Livshysts says. “It will allow me to hire a postdoc, as well as organize a series of workshops for junior researchers, aimed to help others early in their career.”

**Atlanta, GA**

The National Science Foundation (NSF) has awarded a Research Training Groups (RTG) grant to the Georgia Tech Geometry and Topology (GTGT) group. GTGT will use the $2.1 million grant over five years to train undergraduates, graduate students, and postdoctoral fellows. The GTGT project supports NSF’s long-range goal to increase the number of U.S. citizens, nationals, and permanent residents pursuing careers in mathematics.

School of Mathematics faculty members Igor Belegradek, John Etnyre, Stavros Garoufalidis, Mohammad Ghomi, Jennifer Hom, Thang Le, Dan Margalit, and Kirsten Wickelgren make up GTGT and are co-principal investigators of the grant.

**Why Study Topology and Geometry **

Etnyre answers this question. He explains:

“Topology is the study of spaces. They can be the space we live in or configurations of mechanical systems. Mathematicians also consider spaces of solutions to algebraic equations and partial differential equations, as well as even more abstract space.

“More specifically topology is the study of spaces where some notion of continuity makes sense. What are these spaces? How can we distinguish one space from another? What interesting properties do specific spaces have? These are the basics questions in topology, whose language pervades much of mathematics, science, and engineering.

“Geometry is, loosely speaking, the study of some kind of structure on a space. Riemannian geometry involves spaces on which you can measure lengths of vectors and the angles in between. Symplectic geometry allows one to study dynamical systems akin to classical mechanics on a space.

“Topology and geometry underlie a great deal of science and engineering. Whether trying to understand general relativity and the structure of the universe, design robust sensor networks, unravel DNA recombination, develop string theory, or countless other endeavors, the underlying language and ideas are likely to be that of geometry and topology.”

“Topology and geometry underlie a great deal of science and engineering. Whether trying to understand general relativity and the structure of the universe, design robust sensor networks, unravel DNA recombination, develop string theory, or countless other endeavors, the underlying language and ideas are likely to be that of geometry and topology.”

**Expected Outcomes **

Over its five-year run, the grant will enable the training of 60 undergraduate students, 22 graduate students, and 14 postdoctoral fellows. Supplementary funding from the College of Sciences will ensure three years of support for all postdoctoral fellows.

Etnyre says GTGT will leverage its access to Georgia Tech’s engineering programs to spark collaborations between engineers and mathematicians. Similarly, GTGT will use its proximity to institutions serving groups underrepresented in mathematics to help increase the representation of minorities and women in advanced mathematics.

Ultimately, Etnyre says, “we aim to develop students and postdoctoral fellows who are well-rounded scholars, accomplished teachers, and valuable members of the mathematics community.”

**Areas of Expertise**

The GTGT group is strong in various fields:

- Algebraic Topology: Kirsten Wickelgren
- Contact and Symplectic Topology: John Etnyre
- Geometric Group Theory: Igor Belegradek and Dan Margalit
- Global Riemannian and Differential Geometry: Igor Belegradek, John Etnyre, and Mohammad Ghomi
- Heegard-Floer Theory: John Etnyre and Jennifer Hom
- Low-Dimensional Topology: John Etnyre, Stavros Garoufalidis, Jennifer Hom, Thang Le, and Dan Margalit
- Quantum Topology: Stavros Garoufalidis and Thang Le
- Riemannian Geometry of Submaniforlds: Mohammad Ghomi

All these areas would benefit from the grant.

“We aim to develop students and postdoctoral fellows who are well-rounded scholars, accomplished teachers, and valuable members of the mathematics community.”

**Grant-Enabled Activities**

The grant enables the GTGT group to embark on several major activities:

- Expand the group by supporting graduate and postdoctoral fellowships
- Enhance educational opportunities for all students through new courses, expanded seminars and REU (Research Experiences for Undergraduates) opportunities, and a direct-reading program for undergraduates
- Firmly establish the annual Georgia Tech Topology Conference and the biennial Topology Students Workshop, continue the Southeastern Undergraduate Mathematics Workshop, and initiate the Georgia Tech Topology Summer School
- Strengthen professional development components of graduate and postdoctoral training
- Increase interaction with colleges and universities serving groups that are underrepresented in mathematics and expand outreach to precollege students
- Create a website to serve as repository of resources

**Atlanta, GA**

The 2012 speaker is Dr. Emmanuel Candès from Stanford University. He holds the Simons Chair in Mathematics and Statistics. His research areas include: compressive sensing, mathematical signal processing, computational harmonic analysis, multiscale analysis, scientific computing, stastistical estimation and detection, high-dimensional statistics. Applications to the imaging sciences and inverse problems. Other topics of recent interest include theoretical computer science, mathematical optimization, and information theory.

There will be two lectures. One (for a general audience) will be on September 10, at 4:25 pm, in Clough Commons, Room 144. Another one will be at 11:05 am on September 11 in Skiles 006.

Lecture 1: General Audience

### Robust principal component analysis? Some theory and some applications

This talk is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program. This suggests the possibility of a principled approach to robust principal component analysis since our methodology and results assert that one can recover the principal components of a data matrix even though a positive fraction of its entries are arbitrarily corrupted. This extends to the situation where a fraction of the entries are missing as well. In the second part of the talk, we present applications in computer vision. In video surveillance, for example, our methodology allows for the detection of objects in a cluttered background. We show how the methodology can be adapted to simultaneously align a batch of images and correct serious defects/corruptions in each image, opening new perspectives.

Lecture 2: Mathematics Lecture

### PhaseLift: Exact Phase Retrieval via Convex Programming

This talks introduces a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations together with ideas from convex programming to recover the phase from intensity measurements, typically from the modulus of the diffracted wave. We demonstrate empirically that any complex-valued object can be recovered from the knowledge of the magnitude of just a few diffracted patterns by solving a simple convex optimization problem inspired by the recent literature on matrix completion. More importantly, we also demonstrate that our noise-aware algorithms are stable in the sense that the reconstruction degrades gracefully as the signal-to-noise ratio decreases. Finally, we present some novel theory showing that our entire approach may be provably surprisingly effective.

**Atlanta, GA**

Professor Howie Weiss is the Georgia Power Professor of Excellence from Science this year. He was featured at the October 20, 2012 Georgia Tech vs. Boston College football game. The Athletic Association continues the "Professor of the Excellence" program at each home football game this season. The corporate sponsorship this year is Georgia Power.

At each game, one professor will be highlighted, a picture on the scoreboard, information about their research is read to the crowd, etc. A professor from each college will be selected for each of the next six home games.

Weiss' research interests include mathematical biology, analysis, dynamical systems as well as geometry and topology. He is currently working on a $1.3M study with Emory University and Delta Airlines to analyze the transmission of infectious diseases on aircraft. The study is being funded by Boeing.

The benefits to the faculty member are:

- Their research is featured at the game and through the website
- They receive tickets to attend the game where they are recognized
- The faculty member is honored on the field during the game between quarters
- Georgia Power will make a donation of $1,000 in their name to their college
- Each Professor of Excellence receives a football autographed by Coach Johnson

**Atlanta, GA**

Twelve faculty from Georgia Tech's School of Mathematics were named today as Fellows of the American Mathematical Society (AMS). The listing represents the society's inaugural class and includes 1,119 fellows from more than 600 institutions.

The faculty from Tech include math professors: Matt Baker, Jean Bellissard, John Etnyre, Wilfrid Gangbo, Michael Lacey, Michael Loss, Doron Lubinsky, Prasad Tetali, Robin Thomas and associate professor Brett Wick. Adjunct math professors who were recognized also include Bill Cook, from the School of Industrial and Systems Engineering, and Dana Randall, from the School of Computer Science.

“I am delighted that such a large number of Georgia Tech faculty members have been named as Fellows of the AMS,” said Doug Ulmer, chair of the School of Mathematics. “It is an indication of the quality of work being done here and its impact in the wider world.”

The Fellows of the AMS designation recognizes members who have made outstanding contributions to the creation, exposition, advancement, communication and utilization of mathematics. Among the goals of the program are to create an enlarged class of mathematicians recognized by their peers as distinguished for their contributions to the profession and to honor excellence.

“The AMS is the world's largest and most influential society dedicated to mathematical research, scholarship and education,” said AMS President Eric M. Friedlander. “Recent advances in mathematics include solutions to age-old problems and key applications useful for society. The new AMS Fellows Program recognizes some of the most accomplished mathematicians - AMS members who have contributed to our understanding of deep and important mathematical questions, to applications throughout the scientific world and to educational excellence.”

To see the names of individuals who are in this year's class, their institutions, and a description of the fellows program, visit www.ams.org/profession/ams-fellows