REGS: Research Experiences for Graduate Students

University of Illinois at Urbana-Champaign, Department of Mathematics


The purpose of REGS is to encourage research activities at an early stage of he graduate program. The REGS program was conceived by the Graduate Affairs Committee in 2002-3 as part of CID discussions. In 2003, twenty one first and second year graduate students worked on research projects with faculty in various formats. The norm was one or two graduate students working with one or two faculty. Twelve of these students were domestic and were supported by NSF special funding at $3,200 each. The remaining students were supported at the same level by other fundings ources.

The REGS program continued in Summer 2004 and 32 graduate students participated. In the two years, 46 students and 25 faculty members have participated.

The primary goal of REGS is to engage (mathematically) younger graduate students in the research agenda of the Mathematics Department and to thereby increase their maturity level. Such students are then prepared to participate in deeper research projects.

Click on the link below. You will find a list of all the REGS done at UIUC during summer 2004 and detailed summaries (written by the student participants) of most of the projects. You will see considerable variation in the kind of projects and the results obtained in them.

REGS 2004 Summaries

An Interesting Example From 2004

Professor Doug West ran a group REGS on extremal problems in combinatorics involving twenty students in Summer, 2004. The fourteen mathematics graduate students included five at early stages, three at middle stages, and six at an advanced level. Four graduate students from Computer Science and two undergraduates supported with REU funding also participated. The students researched and presented lectures on the current status of various open problems and then settled down to work on problems in small groups. The entire group met for six to nine hours per week and West offered suggestions and encouragement. The results will produce four to six publishable papers. The group is continuing to meet (less intensively) during the academic year, with the participation of several new graduate students.

Summary PDF file
Click for detailed information.

Some Examples From 2003

Professor Dan Grayson led a group of five graduate students from his course on algebraic K- theory into a Summer REGS project. Grayson is writing a graduate text on the subject and wished to give a more manageable presentation of a particularly thorny topic. He divided up the workload among the students and served as their mentor. The end result was an article accepted for publication in Journal of Algebra jointly written by the five students and Grayson.

Professor Scott Ahlgren worked with two students on separate projects in number theory. Each student wrote up his own results at the end of summer. One has been accepted for publication in Journal of Number Theory. Both projects were successful in that they helped their respective student researchers achieve a higher level of confidence and understanding of the commitment one needs in undertaking scientific research.

Professor John D'Angelo worked with Tamas Forgacs on complex variables analogues of Hilbert's 17th problem. During the summer D'Angelo advised Forgacs to take a graduate course from Varolin on Riemann surfaces in the following fall.

As a result Forgacs has chosen Varolin to be his thesis advisor. In this case, the REGS program did not result in a published paper, but did succeed in focusing the student's interests and in the early choice of advisor.

2004 Participants

Advisors are indicated in parentheses, often with the subject of study following.

  • Shivi Bansal (Sather-Wagstaff) - Computations in Commutative Algebra and Algebraic Geometry with Macaulay 2
  • Sylvia Carlisle (Pillay)- Model Theory
  • Thomas Carty (Muncaster)- Applied Dynamical Systems
  • Xiangyu Cheng (Zhu)
  • Jeong-Ok Choi (West)- L(2,1) Labeling Problem
  • Colin Ferguson (Robinson)
  • Tamas Forgacs (Varolin)- Characteristics of Hyperspace
  • Chadwick Gugg (Berndt)- Q-Series and Modular Functions
  • Hailong Hu (West)- Tree-Thickness Problem of Simple Graphs
  • Tim Huber (Berndt)- Q-Series and Modular Functions
  • Kevin Jones (Ando)- Serre Spectral Sequences and Adams Spectral Sequences
  • Samuel Kadziela (Sather-Wagstaff) - Macaulay 2
  • Ji Young Kim (Zhu)
  • Malgorzata Konwerska (Junge)
  • Qi Liu (West)- Extremal Problems of Graph Theory
  • Jana Marikova (van den Dries)
  • Nadia Masri (Sather-Wagstaff) - Macaulay 2
  • Lale Ozkahya (West)
  • Melissa Simmons (Reznick)
  • Bart Snapp (Sather-Wagstaff) - Macaulay 2
  • Michael Sommers (Katz)
  • Hua Tao (Song) - Levy Processes
  • Jennifer Vandenbusche (West) - Combinatorics
  • Chunlin Wang (Song) - Levy Processes
  • Yun Wang (Song) - Levy Processes
  • Diana White (Sather-Wagstaff)
  • Joseph Wright (West)
  • Maosheng Xiong (Duursma) - The Size of Selmer Groups for the Congruent Number Problem
  • Gexin Yu (West) - Combinatorics
  • Mohammad Zaki (Berndt)
  • Feng Zhang (Song) - Probability and Stochastic Process: =B1-Stable Process and Corresponding-Potential Theory
  • Wei Zou (Zhu)

  • 2003 Participants

    Supervisors are indicated in parentheses. Students supported by the NSF are noted.

  • James Atkinson (Ahlgren) NSF
  • Timothy Kilbourn (Ahlgren) NSF
  • Tamas Forgacs (D'Angelo) NSF
  • Kevin Jones (Grayson)
  • Youngsoo Kim (Grayson)
  • Andrea Mhoon (Grayson) NSF
  • Rekka Santhanam (Grayson)
  • Barry Walker (Grayson)
  • Chadwick Gugg (Ford and Zaharescu) NSF
  • Andrew Ledoan (Ford and Zaharescu) NSF
  • Bart Snapp (Dutta) NSF
  • Caleb Eckhardt (Henson) NSF
  • Jonathan Webster (Stein) NSF
  • Samuel Kudziela (Duursma) NSF
  • Ricardo Rojas (Duursma) NSF
  • Christopher Lee (Lerman) NSF
  • Related informal supported research activity:

  • Ayham Gunaydin (van den Dries)
  • Maciej Malicki (Solecki)
  • Salih Azgin (Pillay)
  • Shivi Bonsal (Junge)
  • Jung Jin Lee (Junge)

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