VIGRE

REGS (Research Experiences for Graduate Students)

ALPs

During the Spring 2003 semester, the department's Graduate Affairs Committee, under the leadership of Professor John D'Angelo, developed a summer research program targeted towards first and second year graduate students in mathematics. The program was titled "Research Experience for Graduate Students" (REGS). The National Science Foundation agreed to finance the domestic portion of the project through a supplement to the department's VIGRE program. This funding helped to finance the REGS program held in Summer 2003 and Summer 2004.

The primary goal of REGS is to engage beginning graduate students in the mathematical research agenda of the department, and to thereby increase their maturity level; such students are then better prepared to participate in deeper research projects. We describe three of the REGS from Summer 2003 in detail here to give some idea of the variety and range of styles in the various REGS.

• Professor Daniel 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 an advisor.

1. Kevin Jones, Andrea Mhoon, Rekha Santanam, Young-Soo Kim (Faculty supervisor: Daniel Grayson) Project: graduate text on algebraic k-theory
2. James Atkinson and Timothy Kilbourn (Faculty supervisor: Scott Ahlgren) Project: separate projects in number theory
3. Tamas Forgacs (Faculty supervisor: John D'Angelo) Project: On complex variables analogues of Hilbert's 17th problem
4. Chadwick Gugg and Andrew Ledoan (Faculty supervisors: Kevin Ford and Alexandru Zaharescu) Project: Integers expressible in the form p + gk
5. Samuel Kadziela (Faculty supervisor: Iwan Duursma) Project: Constructing elliptic curves for cryptography
6. Jonathan Webster (Faculty supervisor: Andreas Stein) Project: Arithmetic in cubic function fields and nested squares
7. Caleb Eckhardt (Faculty supervisor: C. Ward Henson) Project: Relationship between bounded operators on Hilbert spaces and their non-standard hulls
8. Ricardo Rojas (Faculty supervisor: Iwan Duursma) Project: Factoring integers of the form mk + a, k E{4,5,7}, using Zhang's special quadratic sieve
9. Christopher Lee (Faculty supervisor: Eugene Lerman) Project: symplectic/contact geometry
10. Bart Snapp (Faculty supervisor: Sankar Dutta) Project: commutative algebra
11. Maciej Malicki (Faculty supervisor: Slawomir Solecki) Project: topological group theory
12. Shivi Bansal (Faculty supervisors: Marius Junge and Andreas Stein) Project: analysis; vector-valued integration; algebraic geometry
13. Salih Azgin (Faculty supervisor: Anand Pillay) Project: group configuration for stable theories
14. Ayhan Gunaydin (Faculty supervisor: Lou van den Dries) Project: elementary theory of the fields of complex and real numbers
15. Jung Jin Lee (Faculty supervisor: Marius Junge) Project: vector-valued integration

Summer 2004 REGS
2004 REGS Reports (in pdf format)

1. Shivi Bansal and Diana White (Faculty supervisor: Sean Sather-Wagstaff) Computations in Commutative Algebra and Algebraic Geometry with Macaulay 2
2. Sylvia Carlisle (Faculty supervisor: Anand Pillay) Model Theory
3. Thomas Carty (Faculty supervisor: Robert Muncaster) Applied Dynamical Systems
4. Xiangyu Cheng (Faculty supervisor: Judy Zhu) Factors Affect Benefit Payment of Medicare Beneficiaries
5. Jeong-Ok Choi (Faculty supervisor: Douglas B. West) L(2,1) Labeling Problem
6. Colin Ferguson (Faculty supervisor: Derek Robinson) Chain conditions on subnormal subgroups
7. Tamas Forgacs (Faculty supervisor: Dror Varolin) Characteristics of Hyperspace
8. Chadwick Gugg (Faculty supervisor: Bruce Berndt) Q-Series and Modular Functions
9. Hailong Hu (Faculty supervisor: Douglas B. West) Tree-Thickness Problem of Simple Graphs
10. Tim Huber (Faculty supervisor: Bruce Berndt) Q-Series and Modular Functions
11. Kevin Jones (Faculty supervisor: Matt Ando) Serre Spectral Sequences and Adams Spectral Sequences
12. Samuel Kadziela (Faculty supervisor: Sean Sather-Wagstaff) Macaulay 2
13. Ji Young Kim (Faculty supervisor: Judy Zhu) Saving the Uninsured
14. Malgorzata Konwerska (Faculty supervisor: Marius Junge) Noncommutative probability
15. Qi Liu (Faculty supervisor: Douglas B. West) Extremal Problems of Graph Theory
16. Benjamin Lundell and Lason McCullough (Faculty supervisor: Iwan Duursma) A generalized floor bound for the minimum distance of geometric Goppa codes and its application to two-point codes
17. Jana Marikova (Faculty supervisor: Lou van den Dries)
18. Nadia Masri (Faculty supervisor: Sean Sather-Wagstaff) Macaulay 2
19. Lale Ozkahya (Faculty supervisor: Douglas B. West) Combinatorics: extremal graph theory, partially ordered sets, graph coloring
20. Melissa Simmons (Faculty supervisor: Bruce Reznick) Introduction to the study of the distribution of lattice points in lattice simplices in R2 and R3
21. Bart Snapp (Faculty supervisor: Sean Sather-Wagstaff) Macaulay 2
22. Michael Sommers (Faculty supervisor: Sheldon Katz) Gromov-Witten theory
23. Hua Tao (Faculty supervisor: Renming Song) Levy Processes
24. Jennifer Vandenbusche and Gexin Yu (Faculty supervisor: Douglas B. West) Combinatorics
25. Chunlin Wang (Faculty supervisor: Renming Song) Levy Processes
26. Yun Wang (Faculty supervisor: Renming Song) Levy Processes
27. Joseph Wright (Faculty supervisor: Douglas B. West) Extremal problems in combinatorics
28. Maosheng Xiong (Faculty supervisor: Iwan Duursma) The Size of Selmer Groups for the Congruent Number Problem
29. Mohammad Zaki (Faculty supervisor: Bruce Berndt) Number theory: Theory of special functions and q-series
30. Feng Zhang (Faculty supervisor: Renming Song) Probability and Stochastic Process: a-Stable Process and Corresponding Potential Theory
31. Wei Zou (Faculty supervisor: Judy Zhu) Social Security Program Survey

Summer 2005 REGS
2005 REGS Reports (in pdf format)

1. Michael Barrus (Faculty supervisor: Douglas West)
2. Marc Harper (Faculty supervisor: Phillip Griffith)
3. Benjamin Lundell (Faculty supervisor: Phillip Griffith)
4. Nadia Masri (Faculty supervisor: Scott Ahlgren)
5. Mark Norfleet (Faculty supervisor: Sergei Ivanov)
6. Partick Reynolds (Faculty supervisor: Sergei Ivanov)
7. Brent Solie (Faculty supervisor: Sergei Ivanov)
8. Michael Sommers (Faculty supervisor: Sheldon Katz )
9. Andrew Suk (Faculty supervisor: Douglas West)
10. Patrick Szuta (Faculty supervisor: Leon McCulloh)
11. Jennifer Vanderbussche (Faculty supervisor: Douglas B. West)
12. Daniel Zaharpol (Faculty supervisor: Phillip Griffith)

Summer 2006 REGS
2006 REGS Reports (in pdf format)

1. Leila Fuladi (Faculty supervisor: Alexander Tumanov) Asymptotics of the Burgers Type Equations
2. Aaron Hill (Faculty supervisor: Burak Erdogan) Harmonic analysis
3. William Green (Faculty supervisor: Burak Erdogan) Fourier analysis
4. Changyoung Jun (Faculty supervisor: Jang-Mei Wu) Pursuit and evasion curves
5. Jason Elliot (Faculty supervisor: Derek Robinson) Group extensions
6. Patrick Szuta (Faculty supervisor: Randy McCarthy) Commutative ring theory
7. Nathaniel Stapleton (Faculty supervisor: Randy McCarthy) Cohomology groups
8. Tim LeSaulnier (Faculty supervisor: Douglas B. West) Open problems in combinatorics
9. Noah Prince (Faculty supervisor: Douglas B. West) Mobile eternal security numbers of graphs
10. Suil O (Faculty supervisor: Douglas B. West) Circular chromatic number of Kneser graph
11. Hehui Wu (Faculty supervisor: Douglas B. West) Tutte's 3-flow conjecture
12. Xiong Lin (Faculty supervisor: Rick Gorvett) Risk measurement
13. Zhengwei Sun (Faculty supervisor: Eduard Kirr) The Limit of Schrodinger Equation with Random Potentials
14. Scott Weaver (Faculty supervisor: Maarten Bergvelt) Vertex algebras
15. Shichang Song (Faculty supervisor: C. Ward Henson) Logic