VIGRE

RAPs (Research Among Peers)

ALPs

Under supervision of the VIGRE administrative team, two additional types of peer groups have been formed to carry out mentoring and interpersonal, professional support. The first type of group is Across Level Peers (ALPs) which includes undergraduate students, graduate students, and faculty of all types in groups to pursue a variety of agendas allowing for a wide-ranging discussion of career plans, and to give general personal support. The other type of group is Research Among Peers (RAPs) which includes graduate students, postdoctoral associates and other faculty. These groups will focus more on the specific research interests of the members, and be a source for consultation in the forming, presentation, and dissemination of research work. Both ALPs and RAPs are meant to be peer groups, but not necessarily peers in the sense of age or professional development peers. They are peer groups in the sense of being aligned by common interests and objectives.

Research Among Peers (RAPs)

The core charge for the RAP groups is to provide a vertical integration structure among graduate students, postdoctoral associates and faculty with similar interests. These groups will be chosen with the understanding that they will be able to exchange mathematical information fairly readily because the individuals are closer to being of similar career development and interests than those in an ALP. Though these groups are meant to be aligned as well as possible with research interests, cross-area connections within mathematics are strongly encouraged especially when in areas where there have been benefits in the past for collaboration of this type.

RAPs are intended to be focal groups for the VIGRE postdoctoral associates. This smaller, research oriented group brings together graduate students, postdoctoral associates and faculty with similar research interests. The RAP groups are working seminars that consist of regular faculty, postdoctoral faculty, and graduate students. RAP organizers are regular or postdoctoral faculty members.

Below are descriptions of specific RAPs held to date.

Fall 2000-Spring 2001

1. Professors Steve Bradlow and William Haboush, and Dr. Luis Alvarez-Consul, a Doob Research Assistant Professor, together with the graduate students Donghoon Hyeon and Yong Fu, conducted an RAP in Bundles and Moduli Spaces (see www.math.uiuc.edu/-hyeon/rap/rap.html).
2. Professor Anand Pillay, Dr. Wai Yan Pong, a Doob Research Assistant Professor, together with graduate students conducted an RAP in Shelah's simple theories in logic. The graduate students participating were Jerry Gagelman, Rahim Moosa, Amador Martin-Pizarro, Thomas Rohwer, and James Tyne. The group used the recent book Simple Theories by Frank Wagner as one of the material sources.
3. Professor Nigel Boston and graduate students conducted an RAP in algebraic number theory. The topic was modular curves. Prof. Boston has been interested in the past few years in studies in cryptography and coding. Together with Prof. Richard Blahut from the Department of Electrical and Computer Engineering (ECE), and other faculty members in the Department of Mathematics and ECE, Prof. Boston has received funding from UIUC and NSF for the UIUC cryptography program. This RAP is in line with this new interdisciplinary mathematical program. The faculty participants were Profs. Nigel Boston, Iwan Duursma, Alexandru Zaharescu. The postdoctoral faculty participating were Marcin Mazur and Sean Sather-Wagstaff. The graduate students who participated were Michael Bush, Jinhee Yi, SorooshYazdani, Kevin O’Bryant, Alison Champion, and James McLaughlin.
4. Dr. Margaret Symington (now at Georgia Tech), a postdoctoral visiting lecturer at UIUC (1999-2001), Prof. Sue Tolman, and Dr. Maria Basterra, a Doob Research Assistant Professor, together with graduate students (Andrew Mauer-Oats, Kristine Baxter, River Chiang) conducted an RAP in symplectic geometry. The RAP was titled, “Problems and research directions in algebraic topology and symplectic geometry.”
5. Professors Stephanie Alexander, Ilya Kapovich, and Paul Schupp conducted an RAP in geometry and hyperbolic groups. The title of this RAP was "Spaces on non-positive curvature." The main participants were Professors Stephanie Alexander, Ilya Kapovich, and Paul Schupp and Doob Research Assistant Professor Peter Brinkmann. The goal was to study in detail several topics from the recent book of M. Bridson and A. Haefliger on CAT(0)-spaces. The group hopes to obtain new results in this area, in particular to prove new types of “glueing” and “combination” theorems for CAT(0) groups. This RAP was of interest especially to students studying group theory and Riemannian geometry. See the RAP webpage at www.math.uiuc.edu/~kapovich/rap1.html.
6. Professors Douglas West and Alexandr Kostochka, Dr. Dmitry Fon-Der-Flaass (a visiting faculty member), and Dr. Jozef Skokan, a VIGRE Research Assistant Professor, conducted an RAP in combinatorics with a focus on graph theory. They had widespread participation from graduate students in combinatorics. These students included Hirotsugu Asari, Weiting Cao, Jeong Ok Choi, Kyung-Won Hwang, Jeong-Hym Kang, Seog-Jin Kim, Kittikorn Nakprasit, Hemanshu Kaul, Michael Pelsmajer, Radhika Ramamurthi, and Naeem Sheikh.
7. Dr. Margaret Symington also conducted an RAP on Problems in Geometry. The graduate students and the faculty participants presented a variety of research level problems in geometry for general discussion. Methods of approach to these problems and related questions were the focus of discussion. The participants included Dr. Maria Basterra, a Doob Research Assistant Professor, and graduate students Kristine Baxter, River Chiang, and Andrew Mauer-Oats. In addition, this RAP conducted two successful panel discussions: “On the Job Market” and “Finding a Research Problem.” The panelists were drawn from mathematics faculty at UIUC. See Good Advice for Beginning Research Careers, that was part of the report generated by this RAP group.

Fall 2001-Spring 2002

1. Peter Brinkmann and Nadya Shirokova(Doob postdoctoral faculty members) led an RAP in knot theory in Fall 2001 and Spring 2002. The group focused on material from two standard texts, Knots by Burde and Zieschang and Knots and Links by Rolfson. Participants in this successful RAP included Doob postdoctoral faculty Brinkmann and Shirokova, faculty members George Francis, Ilya Kapovich, Paul Schupp, John Sullivan, and Kim Whittlesey; and graduate students Elizabeth Denne, Brad Edge, and Katharine Preedy. See the  Knot Theory RAP webapage for more information.
2. Bill Haboush and Maarten Bervelt, faculty members conducted an RAP in representation theory and complex geometry in Fall 2001. They used material from Asterisque 100 and material on D-modules for the focus of their activities.
3. John D'Angelo (faculty member) conducted an RAP in several complex variables in Fall 2001. Regular participants included faculty members D'Angelo, A. Tumanov, and R. Kaufman; Bernhard Lamel (Doob postdoctoral faculty member), and Jae-Seong Cho (graduate student). For part of the year the RAP discussed some of the uses of commutative algebra in several complex variables. Additional participants for this part included Phillip Griffith (faculty member), Sean Sather-Wagstaff (VIGRE postdoctoral faculty), David Murphy (graduate student), and Diana White (graduate student). Topics discussed in the RAP included function algebras, mapping problems in several complex variables, intersection multiplicities for holomorphic mappings, etc.
4. Robert Bauer (faculty member) led an RAP in Fall 2001 that concentrated on conformal invariance, intersection exponents of Brownian motion, and critical planar percolation. The group worked through seminal papers of Lawler, Schramm, and Werner. See the   Conformal Invariance, Intersection Exponents and Critical Percolation RAP webpage for more information.
5. Susan Tolman and Eugene Lerman (faculty members) conducted an RAP in fall 2001 on contact and symplectic geometry and group actions. They worked together with a group of graduate students to study the classification problems of such group actions and applications of this to completely integrable systems.
6. Marco Schlichting (J. L. Doob postdoctoral faculty member) is conducted an RAP in étale cohomology during Fall 2001. Two important cohomology theories are the Zariski cohomology and the étale cohomology. Milne’s book was the primary source for the seminar’s discussions. The RAP required a good deal of background material from algebraic geometry. It was successful because all the necessary background was covered to make it possible for the participants to use étale cohomology in future work. This RAP had 9 active participants, 4 graduate students, 3 postdoctoral faculty members, and 2 regular faculty members. The exact schedule including the title of the talks can be found at   www.math.uiuc.edu/~mschlich/seminars/etale.html.
7. Marius Junge (faculty member) supervised an RAP on noncommutative Lp spaces and modules in Fall 2001 and Spring 2002. Participants in this RAP included faculty members Zhong-Jin Ruan, Florin Boca, Don Burkholder, Marius Junge, and David Sherman (a VIGRE postdoc); graduate students Anthony (Kheyew) Yew, Magdalena Musat, Pedro Poitevin, and Andrew Rizzo; and colleagues from Illinois State University in Normal, Tony Falcone and Michael Marsalli. The participating graduate students gave talks, as did the faculty members. N. Randrianantoanina, a visiting faculty member from Oxford, Ohio, gave one of the talks. See the   Noncommutative L_p Spaces RAP webpage for more information.
8. Robert Fossum (faculty member) supervised an RAP on the algebra and geometry of computer vision in Spring 2002. He is co-organized this RAP with Yi Ma from the Department of Electrical Engineering. Several faculty members and 6-10 graduate students participated in this activity. See the  Geometry and Algebra in Computer Vision RAP webpage for more information.
9. Slawek Solecki (faculty member) led an RAP on descriptive set theory and Rosenthal compacta in Fall 2001 and Spring 2002. Participants in this RAP included Salwek Solecki (faculty member); Wai Yan Pong and Yevgeniy Vasilyev (Doob postdoctoral faculty); and Gosia Konwerska, Dominika Polkowska, Thomas Rohwer, and Maya Saran (graduate students).
10. Marco Schlichting (J. L. Doob postdoctoral faculty member) and Sean Sather-Wagstaff (VIGRE and NSF postdoctoral faculty member) organized an RAP on intersection theory in Spring 2002. A number of graduate students a faculty members worked together reading Fulton’s book on the topic. See the  Intersection Theory RAP webpage for more information.
11. Dr. Sean Sather-Wagstaff, a VIGRE Research Assistant Professor, in conjunction with Professors Phillip Griffith and Sankar Dutta, organized an RAP in commutative ring theory in Fall 2001 and Spring 2002. The group has plans for continuing this activity and for rotating supervision of the RAP over a period of several years. The regular participants were Andrew Richardson (graduate student), Bin Wang (graduate student), Sankar P. Dutta (faculty), Graham Evans (faculty), Robert M. Fossum (faculty), Phillip Griffith (faculty), Jinjia Li (graduate student), Per Jensen (graduate student), Sandra Marie Spiroff (graduate student), Sean Sather-Wagstaff (VIGRE postdoctoral faculty), Wei He (graduate student), Marco Schlichting (Doob postdoctoral faculty). See the Commutative Ring Theory RAP webpage for more information.
12. Nigel Boston (faculty member) organized an RAP on the Langlands Program that has been attended by several regular faculty members, postdoctoral faculty members, and graduate students. For further information about this working seminar, see  www.math.uiuc.edu/~boston/langlands.html.
13. Ilya Kapovich (faculty member) conducted the RAP on "Metric Spaces of Non-Positive Curvature." This was a continuation of the RAP that was begun in Fall 2001. Participants included Ilya Kapovich, Stephanie Alexander, Paul Schupp, Richard Bishop, David Berg, John Sullivan, Peter Brinkmann and Kim Whittlesey. Participating graduate students included Brad Edge, Craig Davis, Jeremony Wong, Bogdan Petrenko, and Elizabeth Denne. See the  RAP on Spaces of Non-Positive Curvature webage for more information.
14. Bruce Berndt (faculty member) directed an RAP in number theory. This group met once a week. Either Bruce Berndt presented open problems suitable as research problems for the participants or the other participants talked on their own work or topics from Basic Hypergeometric Series by N. J. Fine. Regular participatants in this RAP included postdoctoral faculty Jinhee Yi, Guemlan Choi, and Ae Ja Yee; and graduate students Song Heng Chan, Jimmie McLaughlin, Sarachai Kongsiriwong, Heekyoung Hahn, Yelda Aydin, Hamza Yesilyurt, Boon Yeap.
15. Sheldon Katz (faculty member) organized an RAP on quantum cohomology in Fall 2001. The group went through the expository paper of Fulton and Pandharipande on Stable Maps and Quantum Cohomology. The participants were regular faculty members, postdoctoral faculty members, and graduate students. As a result of this RAP, the two graduate students J. Cox and Y. Fu selected stable maps/quantum cohomology for their thesis work under the supervision of Sheldon Katz. See the  RAP on Quantum Cohomology webage for more information.
16. Sheldon Katz (faculty member) organized an RAP in algebraic geometry in Spring 2002. In this RAP, graduate students presented talks on research papers. Emphasis is placed on papers related to their individual thesis work. Also, postdoctoral faculty members occasionally give talks. The group covered a wide range of topics including the minimal model program (Mori theory), stable maps, birational geometry, and equivariant cohomology. See the  Algebraic Geometry RAP webpage for more information.
17. Alica Miller, a VIGRE postdoctoral faculty member, organized an RAP in minimal dynamical systems during spring 2002. The group consisted of postdoctoral faculty members Miller and Karen Shuman, faculty members Joseph Rosenblatt and Svetlana Butler, and graduate students Lina Avramidou and Ciprian Demeter. They jointly presented the background needed to generalize certain results on one-parameter minimal dynamical systems to more generally abelian actions.
18. Zoltan Furedi (faculty member) conducted an RAP on open problems in extremal combinatorics broadly. The organizer supplied problems for the participants to present and directed the discussions toward feasible methods of approaching solutions to these problems.
19. Douglas West (faculty member) conducted an RAP entitled "Structured Families of Graphs" during Summer 2002. Lecturers included graduate students Participants included Jacent Tokaz, Yi-Wei Teo, Luigi Marini, Hailong Hu, Weiting Cao, Miriam Szatrowski, Yijia Zhao and Naeem Sheikk. Regular participants included faculty members Dan Grayson and Charles Rezk and graduate students Bin Wang and David Gepner.
20. Bin Wang, with the supervision of his advisor Dan Grayson, organized and conducted a RAP in summer 2002 on motivic cohomology. Several people gave talks during the progress of this working seminar. Regular participants included faculty members Dan Grayson and Charles Rezk and graduate students Bin Wang and David Gepner.

Fall 2002-Spring 2003

1. Piotr Kowalski organized a working seminar in fall 2002 on Separably Closed Fields/Differential Fields in positive characteristic as part of the Logic FRG program. This was the first UIUC FRG RAP.
2. Steve Bradlow organized the Special Holonomy RAP. This Rap focused on Riemannian metrics with special holonomy and differential forms of degrees 2,3, and 4. The text by Nigel Hitchin, Stable Forms and Special Metrics, formed the literature basis of this RAP. Their mission was to explore geometric structures associated with metrics of special holonomy, and related geometric structures (see the website for a list of topics and speakers). There were approximately 10 regular participants, including graduate students in physics and math, one post-doc, and faculty. Faculty: Steve Bradlow (organizer), Rob Ghrist, Sheldon Katz, Eugene Lerman, John Sullivan, Sue Tolman, and Dick Bishop; Post-doc Eric Sharpe; graduate students Jeremy Wong, Thomas Rohwer, Hui Li, Rahul Biswas, Sean Nowling, Mehmet Sahin, Walid Abou Salem.
3. Robert Fossum, Yi Ma, and Yoshi Shinagawa organized a RAP in fall 2002 on the Geometry and Algebra of Computer Vision. This program provides an open forum for gaining a deeper mathematical understanding of geometry and algebra related to computer vision, graphics, imaging, and robotics. The goal is to promote interdisciplinary dialogues and research projects, especially those related to mathematics and engineering of computer vision. See http://decision.csl.uiuc.edu/~yima/RAP.html for more information about this interesting RAP.
4. The RAP on Spaces of Non-Positive Curvature, organized by Ilya Kapovich for Spring 2003 semester, is a continuation of the RAP that was begun in Fall 2001. It is based on the book "Metric spaces of non-positive curvature" by M.Bridson and A.Hefliger. Organizers are: Ilya Kapovich, Stephanie Alexander, Paul Schupp, Richard Bishop, and Kim Whittlesey. More information is available on-line at www.math.uiuc.edu/~kapovich/rap4.html
5. Bruce Berndt organized the Basic Hypergeometric Series with Applications RAP in both Fall 2002 and Spring 2003 semesters. Participants included six graduate students, postdoc Ae Ja Yee, and faculty member Bruce Berndt. Professor Berndt lectured on open problems accessible for students to work on, or the students lectured on their own research, or on material from N. J. Fine's Basic Hypergeometric Series with Applications.
6. Janne Heittokangas conducted a RAP in spring 2003 on Analytic Function Spaces in the Unit Disc with applications to Complex Differential Equations. Different texts and articles were used as the literature basis for this RAP. Regular participants included faculty Janne Heittokangas, Aimo Hinkkanen, Joseph Miles, and graduate students Dong-Il Kim, Xiaosheng Li, and Lia Petracovici.
7. Rinat Kedem conducted a RAP on Quantum Groups and Representations at Roots of Unity in spring 2003. This RAP examines a particular class of algebras that arise naturally in several different contexts. The main references for this interaction are books and articles that have recently been written on the subject.
8. Slawek Solecki conducted a RAP in spring 2003 on Extremely Amenable Groups. This RAP focuses on the continuous actions of Polish groups with particular emphasis on extremely amenable groups. The group used a number of different articles on this exciting area of descriptive set theory and abstract harmonic analysis as a basis for the study.
9. Charles Rezk conducted a RAP on Lubin-Tate-Morava Homology Theories in spring 2002. The goal of this RAP is to learn how the structure of homotopy theory is related to the theory of formal group laws. Mathematical work by J. F. Adams, A. Frölich, and M.J. Hopkins, N.J. Kuhn, and D. C. Ravenel forms the background material for this study.
10. Dror Varolin organized a RAP on Several Complex Variables in academic year 2002-2003. The focus of the RAP is geometric techniques in complex analysis. Specifically, they studied two things: 1) Analytic techniques in algebraic geometry; and 2) CR geometry and the method of attaching disks. Faculty participants included John D'Angelo, Alex Tumanov, Dror Varolin, and graduate student participants included Jae-Seong Cho and David Rose. There were in addition two outside speakers.
11. Robert Bauer organized a RAP on Random Planar Curves, Conformal Invariance, and Schramm-Loewner Evolution in spring 2003. The goal of this RAP was to review was to understand better the recent mathematical results on conformal invariance, scaling limits, and properties of two-dimensional random curves. The lecture series by Wendelin Werner at the 2002 Saint Four Summer School was used as the basis for the text material in this RAP. Active participants are faculty members Donald Burkholder, Renming Song, Dirk Hundertmark, Frank Knight, Rinat Kedem; and graduate students Chunlin Wang, Feng Zhang, Chetan Pahlajani, Kittipat Wong.
12. Robert Ghrist conducted a RAP in spring 2003 on Computational Topology. This joint venture with the Department of Computer Science provides an opportunity for a group of graduate students and faculty members to look closely at what types of algorithms are effective in computing topological quantities, what is the computational complexity of a given topology problem and how conversely topological thinking can impact computational problems.
13. Sheldon Katz led a RAP on String Theory for Mathematicians in spring 2003. The goals of this RAP was to learn the notions of string theory from a mathematical perspective with attention to the progression through the relevant essentials of classical mechanics, quantum mechanics, quantum field theory, and finally string theory. Participants included faculty members and students from the Departments of Physics and Mathematics.
    

Fall 2003-Spring 2004

1. Marius Junge and Nicholas Yannelis (Department of Economics at UIUC) conducted a RAP on vector-valued integration and its connections to economics in Fall 2003. The mathematical background of equilibrium theory with asymmetric information in economics was the central focus of this RAP. Participants included the organizers, Denka Kutzarova, Jerry Uhl, Tom Carty, Melika Bulu, and M. Polarmatchuk.
2. Ilya Kapovich conducted an RAP in Fall 2003, the last semester of the RAP “Metric Spaces of Non-Positive Curvature”. The participants reviewed in detail Richard Schwartz' proof of the Quasi-Isometric Rigidity Theorem for non-uniform lattices in Hⁿ (where n>2). This theorem provided a far-reaching generalization of Mostow Rigidity and also resulted in the birth of a new and active subject of Quasi-Isometric Rigidity. The following people participated in the RAP: (faculty members) Ilya Kapovich (organizer), Stephanie Alexander, Richard Bishop, Paul Schupp, David Berg; (postdoctoral faculty and visitors) Peter Brinkmann, Patrick Bahls, Dan Farley, Kim Whittlesey, (graduate students) Elizabeth Denne, Bogdan Petrenko, Jeremy Wong, Lucas Sabalka, and John Barela. There were also two guest speakers: Gregory Bell from Pennsylvania State University and Alex Furman from the University of Illinois at Chicago.
3. Rinat Kedem conducted an RAP in Fall 2003 on Nakajima’s quiver varieties and representation theory. The group met weekly and worked through a number of aspects of the original work of Nakajima and related work of other mathematicians. The primary participants were Maarten Bergvelt, Steve Bradlow, Richard Corrado, William Haboush, Wei He, Sheldon Katz, Rinat Kedem, David Murphy, Akira Sano, Susan Tolman, Bin Wang, and Xinyun Zhu.
4. Eugene Lerman conducted an RAP in Fall 2003 on SubRiemannian Geometry. The group met twice a week for the whole term. They used Richard Montgomery’s recent book as a guide for the discussions. The participants included Eugene Lerman, Vadim Zharnitsky, Rob Ghrist, Jeremy Tyson, Dror Varolin, Sue Tolman, Steve Bradlow, Ilia Binder, Dick Bishop, Stephanie Alexander, and Howard Osborn.
5. Dror Varolin conducted an RAP in Fall 2003 on several complex variables and Riemannian geometry. Participants included graduate students and faculty members. The speakers included John D’Angelo, Dror Varolin, Alex Tumanov, Adam Coffman (IUPUI Fort Wayne), John McCarthy (Washington University), and Eric Shippers (University of Michigan).
6. Florin Boca conducted an RAP on Expander Graphs (Constructions and Applications) in Fall 2003 and Spring 2004. The aim was to read in detail the book “Elementary Number Theory, Group Theory, and Ramanujan Graphs” by Davidoff, Sarnak and Valette, together with a few more additional topics. Regular participants included Iwan Duursma, Ilya Kapovich, Robert Kaufman, Marius Junge, Alexandru Zaharescu (mathematics faculty members), Pascal Vontobel (CSL postdoctoral faculty member), Ioana Boca, Michael Bush, Negar Kiyavash (graduate students). Other participants included Yevgeny Gordon (Eastern Illinois University faculty member), Patrick Bahls (mathematics postdoctoral faculty member), Dan Farley (mathematics department visitor), Weiting Cao, Lucas Sabalka, Florin Stan (graduate students).
7. Robert Fossum (Department of Mathematics) and Yi Ma (Department of Electrical and Computer Engineering) conducted a RAP on Geometry and Algebra of Computer Vision. This RAP centered on a series of lectures concerning the mathematical foundations for implementing computer vision. Participants included faculty members and graduate students in the Departments of Mathematics and Electrical and Computer Engineering.
8. Scott Ahlgren and Matt Boylan conducted a RAP in spring 2004. The group discussed connections between modular forms, modular curves, Galois representations, and problems in number theory. Participants talked on background material and current research papers. In addition to the organizers, other regular participants included Leon McCulloh and 10-12 graduate students. For more information, go to their webpage www.math.uiuc.edu/~boylan/rap.html.
9. Sheldon Katz conducted a RAP in spring 2004 on supersymmetry from a mathematical perspective. There were talks on supersymmetry and mirror symmetry. The speakers were Sheldon Katz, Steve Bradlow, Rinat Kedem, Richard Corrado, Tom Junk, Josh Guffin, Florin Boca, and Duncan Christie. The regular participants were Elizabeth Denne, Dirk Hundertmark, Chad Fendt, Joshua Guffin, Inga Karliner, Jonathan Cox, Tom Junk, Kevin Kai-feng Chiou, Rob Leigh, Michael Mulligan, Michael Sommers, Sean Nowling, Rinat Kedem, Mehmet Sahin, Michael Stone, Ognyan Stoyanov, Vivek Srikrishnan, and Fu Yong.
10. Sean Sather-Wagstaff conducted a RAP in spring 2004 on Sharp’s Conjecture on dualizing complexes. The goal was to cover background material and the proof of Sharp’s conjecture using the existence of Macaulayfications.
11. Robert Ghrist conducted an RAP on Computational Topology in Spring 2004 in conjunction with the Computer Science department. Regular participants in this RAP included faculty members Rob Ghrist (Math), John Hart [CS], Jeff Erickson [CS], Edgar Ramos [CS], John Sullivan [Math], Kim Whittlesey [Math] and Students David Lipsky [math, grad], Valerie Peterson [math, grad],   Jae Bum Jung [math, grad], Elizabeth Denne [math, grad], Damrong Guoy [CS, grad], Terry Fleury [CS, grad], Lana Lazebnik [CS, grad], David Bunde [CS, grad], Tyler Smith [undergrad], Pat Szuta [undergrad].