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I joined the department of Applied Math in fall 2014. Previously I was a Herman Goldstine Postdoctoral fellow in Mathematical Sciences at IBM Research in Yorktown Heights, NY, and a postdoctoral fellow via the  at Paris 6 (), after doing my doctoral work at .

Websites

For now, information on our research group is scattered across two websites: this current website (not updated often), and also

• my  which I update with new papers and such more regularly (mirrored at )

Research synopses

Broadly speaking, our group is interested in information extraction from various types of datasets. We are part of a hybrid field combining applied math with computer science and signal processing techniques. Some specific topics we research are:

• Optimization: first-order methods, quasi-Newton methods, primal-dual algorithms, convex analysis.
  • Types of problems: from computational imaging, and semi-definite programs (from relaxations, or from robust PCA)
  • Mathematical applications: compressed sensing and variants, matrix completion and variants (robust PCA…), non-negative matrix factorization and end-member detection, sparse SVM
• Numerical linear algebra: randomization and its interplay with optimization methods
• Sampling theory: how to make the best use of your resources when confronted with big data
  • e.g.,
  • e.g.,
• Physical applications: ,Ìý, MRI, medical imaging, IMRT, renewable energy, big-data
  • Recent applications (2015--2018) have been in super-resolution (optical) microscopy and photo-acoustic microscopy

To get a more specific idea of the research our group does, here are some topics we're doing in 2018:

• Parametric and compressive estimation, for phase retrieval (Jessica) in x-ray imaging, and for discovering archaeological ruins (Abby) in radar imaging without creating a DEM
• Theoretical machine learning: sub-sampling and sketching (Farhad, Eric)
• Avoiding/analyzing saddle points in non-convex optimization: for biconvex programming in program analysis and/or controls (Jessica), and for dictionary learning and neural network learning (Leo)
• Improving accuracy of sparse estimation using mixed-integer programming (Eric, Leo)
• Efficient computation of the cross-ambiguity function (CAF) for signal processing, to estimate time-of-arrival of radar signals (James)
• Randomized algorithms for numerical linear algebra and optimization (James, Derek)
• Optimization algorithms in general, and ill-conditioning and pre-conditioning (James, Jessica, Osman)
• Efficient algorithms for GPUs (James, Derek, Jessica)
• Tensor decompositions (Osman, Derek)
• Robust estimation (Richie)
• Misc imaging applications (for optical super-resolution, with Carol Cogswell's group in ECEE; and for photo-acoustic super-resolution, with Todd Murray's group in Mech E)
• Stochastic variance reduction methods for non-linear inverse problems
• Remote sensing of the Chesapeake bay (Cheryl)
• Behavior genetics (Richard, Farhad)

News

• Plans for Summer 2019
  • Internships to be announced soon
• Winter 2018/2019
  • Marc Thomson and Richard Border are doing their Masters theses with the group
  • Liam Madden has joined the group (working also with Emiliano Dall'Anese)
  • Richie Clancy is working on robust optimization
• July 2018: Becker is PI on a 3-year $150k NSF grant in computational math
• July 2018: Becker is Co-PI on Prof. Ken Jansen's ALCF project
  • This gives us early access to the new Aurora supercomputer (the nation's first exascale computer)
• Summer 2018 activities:
  • Will Shand is a new undergrad researcher in our group
  • Zhishen (Leo) Huang is interning with 's group at the Information Sciences Institute at USC
  • Eric Kightley is interning with
  • Jessica Gronski is interning with SavvySherpa
  • Stephen Becker is giving a in the UK () in June, then attending in Bordeaux France in July
  • Osman Malik is attending and in Stockholm, Sweden in July
• Spring 2018: Farhad Pourkamali-Anaraki (PhD then Postdoc in the group) accepts a tenure-track professor job at computer science deparment
• May 2017: Farhad Pourkamali-Anaraki receives his PhD in electrical engineering
• May 2017: Derek Driggs receives his Masters in applied math, and heads to Cambridge for his PhD
• April 2017: Derek Driggs wins the Gates Cambridge scholarship (fully funded PhD at Cambridge, equivalent to a Rhodes scholar for Oxford)
• Summer 2016:
  • Farhad interns with
  • Jessica interns with Tamara Kolda at
  • James interns with
• July 2015, Becker awarded the Beal-Orchard-Hays prize
  • along with Michael Grant and Emmanuel Candes. The prize is awarded every 3 years for outstanding optimization software

CU activities

• September 2019, we have a new website with .
• January 2018, I am one of four founding members of the new Imaging Science center in the engineering college. Here is the new Imaging Science IRT website.
• You may be interested in joining the .
• We run a (Fall 2018, this is usually 3:30 Tuesdays at Newton lab). Anyone is welcome to show up.
  • To receive announcements about talks at the seminar, please sign up for the
• I am also sometimes involved in the .

For K-12 students and educators interested in partnering with CU

Some resources:

• The week-long summer I am involved with (in collaboration with Northrop Grumman, St. Vrain School District, Rangeview HS, and Aurora Public Schools). 2017 in Aurora, and 2018 in Aurora and Longmont
  • any Colorado high schooler can sign up to take the camps
  • Applied Math graduate students help me teach the class
• , a non-profit at CU
• BOLD center (part of the engineering college; "Broadening Opportunity through Leadership and Diversity")
• (part of the engineering college, located next to the engineering building)
• Idea Forge maker space and more
• CU wizards
• many more at the Center for STEM Learning's list of programs.

Thinking about a PhD in Applied Math at CU?

• ÍÃ×ÓÏÈÉú´«Ã½ÎÄ»¯×÷Æ· is a with excellent resources
  • According to NSF data, CU is #13 nationwide in , #7 nationwide by number of , and if you combine with our medical school, we are #20 nationwide in  (other top-10 schools in R&D, like Duke, are already combined with their medical schools).
  • CU is ranked the  by the US News and World Report
    • (2018 update: CU is now #1 in the world for geoscience and #43 overall in the world)
    • #11 internationally in computer science by normalized citation index, #35 overall internationally in physics, etc.
  • From the , CU is the #1 public university for NASA research funds, Colorado is the 2nd largest aerospace economy in the US, and our aerospace program is ranked #8 (graduate) and #10 (undergraduate)
  • Earth and Atmospheric science is ranked #1 globally in 2018
  • 2020 rankings (as of Marh 2020) place APplied Math as #14 nationally
• A unique feature of CU is the strength of our (ATLAS, Biofrontiers, CIRES, INSTAAR, IBS, ICS, JILA, LASP, ... ), as well as the nearby national labs (NOAA, NIST, NCAR)
• Applied Math is at the center of quantitative work in the institutes, as well as new statistical efforts on campus
• We are one of just a handful of specialized Applied Math departments in the US. An applied math degree greatly distinguishes graduates
• Ready to apply? Please apply to our department (we do not do direct admission into a research group)

Thinking about applied math in general?

• See the .

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