Faculty & Staff
Don Bonar was born in Murraysville, WV (Jackson County) on July 7, 1938, the son of Nelson Edward Bonar II and Ada Polk Bonar. He graduated from Ravenswood High School and was awarded a four-year Board of Governors Scholarship to West Virginia University where he received the B.S. in Chemical Engineering in 1960. While at WVU, he was a member of the physics, chemistry, and chemical engineering honoraries, and served as President of Tau Beta Pi, the engineering honorary. Two National Science Foundation Fellowships supported his graduate work in mathematics. He received the M.S. from WVU in 1961 with a major in mathematics and a minor in physics and the Ph.D. from Ohio State University in 1968. His Ph.D. work was in complex analysis. In 1965 Don joined the faculty of Denison University in Granville, OH where he has been teaching mathematics, statistics and computer science.
Awards received include the Richard King Mellon Foundation Award for excellence in teaching and scholarship in 1973 and the Sears-Roebuck Teaching Excellence and Community Leadership Award in 1991. In 1995 he was selected to fill the new fully endowed George R. Stibitz Distinguished Professorship in Mathematics and Computer Science. In 1999 Don was inducted into the Academy of Chemical Engineers at West Virginia University. He is the author of the book entitled On Annular Functions, a co-author of the book Real Infinite Series, and a co-author on several research papers. He has published joint work with the internationally acclaimed Hungarian mathematician Paul Erdos. Community service includes membership on the Granville Foundation, the Granville Development Commission, the Licking County (OH) Joint Vocational School Board (facility recently renamed C-TEC, Career and Technology Education Center of Licking County), and serving as President of the Granville Exempted Village School Board.
Don and his wife Martha Baker Bonar are the parents of Mary Martha, a resident in emergency medicine at the Penn State University Medical Centers in Hershey, PA. Forever Mountaineers, the Bonars enjoy time at their farm, family owned since 1869, in West Virginia.
- Real Infinite Series (with Michael J. Khoury '03) in Mathematical Association of America (MAA). 2006.
- On Annular Functions Daniel D. Bonar, 1971.
Thomas Bressoud worked outside of academia both before and after receiving his Ph.D. from Cornell University in 1996. Before his time in Ithaca, Dr. Bressoud spent 7 years working for MIT Lincoln Laboratory in real-time radar systems. After his Ph.D., Dr. Bressoud worked for a startup, Isis Distributed Systems, and, through the acquisition frenzy of the 90’s, was working for Lucent Technologies when he transferred to their research arm, Bell Laboratories in Murray Hill, NJ.
In 2002, Dr. Bressoud joined the Denison faculty. He enjoys teaching courses across the undergraduate curriculum, from introductory courses exposing students from across campus to the fundamental ideas of computer science to upper level electives. In alignment with his research interests, he particularly enjoys teaching systems classes, like Networking and Operating Systems, and a special topics course in parallel programming and high performance systems.
Selected student research projects:
- Towards a MapReduce Application Performance Model, Jared Gray and Thomas C. Bressoud, Proceedings of the 2012 Midstates Conference on Undergraduate Research in Computer Science and Mathematics (MCURCSM 2012), Delaware, OH.
- The Performance Characteristics of MapReduce Applications on Scalable Clusters, Kenneth Wottrich and Thomas C. Bressoud, Proceedings of the 2011 Midstates Conference on Undergraduate Research in Computer Science and Mathematics (MCURCSM 2011), Granville, OH.
- Investigating Cluster Fault Tolerance: Web Interfaces, Simulation, and Extension, Sarah Mercier and Thomas C. Bressoud. Anderson Summer Research and Denison Summer Scholar Poster Session, 2009.
- The Performance Cost of Virtual Machines on Big Data Problems in Compute Clusters, Neal Barcelo, Nick Legg, and Thomas C. Bressoud, Proceedings of the 2008 Midstates Conference on Undergraduate Research in Computer Science and Mathematics (MCURCSM 2008), Wooster, OH. Also presented to the Big Data research group at Intel Research, Pittsburgh.
My research interests are within the systems area of computer science and can be partitioned into the subareas of (i) fault-tolerance, (ii) networking and inter-domain routing, and (iii) high performance computing. Where possible, I enjoy the pursuit of research at the intersections of these areas. Within fault tolerance, I specialize in "minimally invasive" techniques of transforming non-fault-tolerant systems and protocols and legacy applications into fault-tolerant versions while minimizing impact on the application. In inter-domain routing I work in connection-oriented fault tolerant protocols and in load-balancing techniques for BGP, and in high performance computing, I study the performance of distributed (cluster) systems as we both scale and introduce failures into the system.
- L. Alvisi, T. Bressoud, A. El-Khashab, P. Weidmann. Method, Apparatus And System For Maintaining Connections Between Computers Using Connection-Oriented Protocols. U.S. Patent Number 7,673,038, Awarded March 2, 2010.
- Thomas C. Bressoud and Michael A. Kozuch, Cluster Fault-Tolerance: An Experimental Evaluation of Checkpointing and MapReduce through Simulation. In Proceedings of the IEEE International Conference on Cluster Computing. New Orleans, LA. Oct. 2009.
- Dmitrii Zagorodnov, Keith Marzullo, Lorenzo Alvisi, and Thomas C. Bressoud. Practical and Low-Overhead Masking of Failures of TCP-Based Servers. ACM Transactions on Computer Systems, 27(2):80-107, May 2009.
- Thomas C. Bressoud and M. Frans Kaashoek (MIT). Chairs’ Report on Twenty-First ACM Symposium on Operating Systems Principles. ACM Operating Systems Review, 42(3): pp123-126, April 2008.
- Thomas C. Bressoud, Rajeev Rastogi, Mark A. Smith. System and Method for Optimally Configuring Border Gateway Selection for Transit Traffic Flows in a Computer Network. U.S. Patent Number 7,197,040, Awarded March 27, 2007.
Jessen Havill joined the Denison faculty in 1998, having spent the six prior years studying at The College of William and Mary in Williamsburg, Virginia. Dr. Havill teaches courses across the computer science curriculum, in both theory and systems, although his specialty is in theory-related courses like Discrete Mathematics, Data Structures, and Algorithm Design and Analysis. He is also very interested in developing courses that explore connections between computer science and other disciplines. In 2009, he developed and started teaching a new introductory computer science course (CS 111: Foundations of Computing for Scientific Discovery) that introduces the principles of computer science in the context of scientific modeling and simulation. In 2012, he and Jeff Thompson, a colleague in the Biology Department, began teaching an interdisciplinary computational biology course (CS/BIOL 309: Computational Biology). In 2013, Dr. Havill was awarded Denison’s Charles A. Brickman Teaching Excellence Award.
Selected student research projects:
- Bringing Extinct Sponges to Life: Modeling Stromatoporoid Growth with OpenGL, Trevor Masters, Summer 2013 (co-advised with David Goodwin, Geosciences)
- Improved Upper Bounds for Online Malleable Job Scheduling, Nathaniel Kell, 2012–2013
- A Web Tool for Detecting Riboswitches in Genomic Sequences, Steven Johnson, Summer 2012
- Towards a More Realistic Metric for Online Ring Routing, Andrew Quinn, Summer 2012
- Using Computational Algorithms to Further Examine and Visualize Riboswitch Domains, Joseph Sheets, Summer 2011 (co-advised with Jeff Thompson, Biology)
My research largely focuses on the design and analysis of algorithms for online network routing and machine scheduling problems. An online algorithm is one that processes its input one element at a time instead of all at once like a traditional algorithm. For example, an online room scheduling algorithm would have to assign a room to each event as it "arrives" without knowing what events might need to be scheduled later. Online algorithms usually cannot come up with optimal solutions due to their lack of knowledge about the future. Instead, we try to design algorithms that find solutions that are provably within some factor of optimal. I have also recently developed an interest in problems in computational biology.
- Optimal Online Ring Routing [pdf] (with K. R. Hutson) Networks 57(2), pp. 187-197, 2011
- Online Malleable Job Scheduling for m ≤ 3 [pdf] Information Processing Letters111(1), pp. 31-35, 2010
- An Algorithm for Detecting TPP Riboswitches in Archaea (poster, with C. Bhatiya and J. S. Thompson) Ohio Collaborative Conference on Bioinformatics (OCCBIO), 2009
- Competitive Online Scheduling of Perfectly Malleable Jobs with Setup Times [pdf] (with W. Mao) European Journal of Operational Research187(3), pp. 1126-1142, 2008
- Technically Speaking: Fostering the Communication Skills of Computer Science and Mathematics Students [pdf] (with L. D. Ludwig) In Proceedings of the 38th ACM SIGCSE Technical Symposium on Computer Science Education, pp. 185-189, 2007
After graduating from Penn State with a degree in Computer Engineering and a minor in Philosophy, Dr. Kretchmar worked as a software engineer at IBM to develop their first data warehousing project. In his graduate programs at Rensselaer and Colorado State, Dr. Kretchmar focused on a variety of artificial intelligence and machine learning techniques. His Ph.D. dissertation analyzed a robust (fault tolerant) reinforcement learning controller for a large HVAC system. Dr. Kretchmar teaches a wide range of courses across the computer science curriculum as well as introductory liberal arts mathematics courses. Dr. Kretchmar's classes often experiment with non-traditional pedagogies including a portfolio based system in his Sophomore Data Structures class, and a research paper based Artificial Intelligence seminar. He is also very interested in writing pedagogy and in first year student experiences; he served as Denison's Dean of First Year Students from 2007 to 2012.
Selected Student Research Projects:
- Text Message Authorship Classification Using Support Vector Machines, Yifu Zhou, 2013.
- A Reinforcement Learning Robotic Arm Controller, Taylor Kessler Faulkner, 2013.
- An Analysis of Ballot Ordering for Final Tribal Councils in the Television Series Survivor, Nat Kell. 2010.
- Kernel Methods for Image Processing, Dan Bucatanschi, 2006.
My research area is machine learning techniques. I concentrate in Reinforcement Learning, especially in building controllers for various dynamic systems. Additionally I work in the area of classification techniques including Kernel Machines and Support Vector Machines. I also dabble in games and game theory, and in discrete and combinatorial mathematics.
- Suspense at the Ballot Box. (with Nat Kell) The College Mathematics Journal, Vol 44, No 1. 2013.
- Tree Traversals and Permutations. (with Todd Feil and Kevin Hutson) Congressus Numerantium, Vol 172. 2005.
- Improved Automatic Discovery of Subgoals for Options in Hierarchical Reinforcement Learning. (with Todd Feil and Rohit Bansal) Journal of Computer Science and Technology. October, 2003.
- A Neighborhood Search Technique for the Freeze Tag Problem. (with Dan Bucatanschi, Blaine Hoffman and Kevin Hutson) Extending the Gap: Advances in Computing, Optimization, and Decision Technologies. 2007.
Joan Krone joined the Denison faculty in 1990, having taught mathematics at Ohio Dominican College before earning her Ph.D. in Computer Science from the Ohio State University, where she taught Data Structures and Algorithm Analysis before coming to Denison.
Her research is in the mathematical foundations of computer science, emphasizing mathematical reasoning about the formal specification and verification of software in the context of software engineering principles. Krone is a strong advocate of undergraduate research and has served as mentor to more than 30 undergraduate research students, many of whom have presented their work at professional conferences. She developed a discrete math course that introduced computer science applications of mathematical concepts and co-authored the textbook “Essential Discrete Mathematics for Computer Science” with Todd Feil. In addition to teaching computer science Krone is the Director of the Gilpatrick Center, which oversees the summer research program at Denison, as well as serving to advise students applying for a variety of prestigious scholarships such as Fulbright, Marshall, Rhodes, and others.
Selected Student Research Projects
Welch, D. 2011, 2012 “Modular Design and Verification in RESOLVE,” NSF student.
Presentation at MCURCSM, November 2012.
Behrend, S. 2007. “Logic for Program Verification.” DURF student. Presentation at SIGCSE,
March, 2007. Presentation at MCURCSM, November, 2007.
Fressola, A. 2004. “Integers by Induction.” Anderson student. Presentation at the National American Mathematical Society Conference, Phoenix, Arizona.
Tawney, M. 2003 Anderson student. “Algorithm Analysis for the Object Oriented Paradigm.”
2002. Invited talk at The Ohio State University, March 13, 2003. Posters on the Hill, April 1, 2003.
Dimitrov, V. summer 2001. “Zero-Divisor Graphs.” Presented at the ACM-SIGCSE Conference, February, 2002.
My research lies in the field of formal methods for software engineering. The focus is on the formal specification of software in the context of software engineering principles developed by experts in the field over decades of research and practice. Recent NSF funding has supported the design and development of a new language, RESOLVE (REusable SOftware Langauage with VErification), that includes constructs for formal mathematical specifications to promote mathematical reasoning and proofs of program correctness. Krone’s work has included both the development of logic for reasoning about program correctness and the development of material needed in the computer science curriculum to support mathematical reasoning about programs.
1. Gregory Kulczycki, Murali Sitaraman, Joan Krone, Joseph E. Hollingsworth, William F. Ogden, Bruce W. Weide, Paolo Bucci, Charles T. Cook, Svetlana Drachova, Blair Durkee, Heather Harton, Wayne Heym, Dustin Hoffman, Hampton Smith, Yu-Shan Sun, Aditi Tagore, Nighat Yasmin, and Diego Zaccai, A Language for Building Verified Software Components, Proceedings of ICSR, Pisa, Italy, July 2013.
2. Joan Krone, Jason Hallstrom, Murali Sitaraman, CCSC 2011 Proceedings, “Mathematics throughout the CS Curriculum.”
3. Murali Sitaraman, Bruce Adcock, Jeremy Avigad, Derek Bronish, Paolo Bucci, David Frazier, Harvey M. Friedman, Heather Harton, Wayne Heym, Jason Kirschenbaum, Joan Krone, Hampton Smith, and Bruce W. Weide, “Building a Push-Button RESOLVE Verifier: Progress and Challenges,” Formal Aspects of Computing, 2010, 34 pages.
4. J. Krone, J.E. Hollingsworth, M. Sitaraman, and J.O. Hallstrom, “A Reasoning Concept Inventory for Computer Science,” Technical Report RSRG-10-01, School of Computing, Clemson University, Clemson, SC 29634-0974, September, 2010, 6 pages.
5. Sitaraman, Hallstrom, White, Drachova-Strang, harton, Leonard, Krone, Pak, “Engaging Students in Specification and Reasoning: Hands on Experimentation and Evaluation,” Proceedings of ITiCSE, July 5-8, 2009.
6. Keown, H., Krone, J., & Sitaraman, M. , “Formal Program Verification.” The Encyclopedia of Computer Science and Engineering. Wiley, 2008.
Ashwin Lall joined the Denison faculty in 2010. Prior to this, he was a postdoctoral researcher at Georgia Tech, a Ph.D. student and Sproull fellow at the University of Rochester, and a math/computer science double major at Colgate University. Dr. Lall has taught several introductory courses, such as CS110, CS109, FYS102, as well as advanced topics such as Theory of Computation and Design/Analysis of Algorithms. Dr. Lall created a Game Design elective for the CS major in 2012. In 2013, he designed a new version of the introductory computer science course with an emphasis on applications in the social sciences. Dr. Lall was named a Bayley-Bowen faculty fellow in 2013.
Selected student research projects:
- Yuting Chen, Edward Takahashi. Sketch-guided sampling for measuring network traffic statistics. In proceedings of MCURCSM 2012.
- Edward Takahashi, Yuting Chen. Divergence in network traffic. In proceedings of MCURCSM 2012.
My research focuses on the design and analysis of algorithms for very large data sets. Much of my work has to do with applications in computer networks, though I have also done work in the areas of databases, social networks, distributed computing, and natural language processing (AI). I am interested in doing summer research with students on analysis of networking data, query optimization, or social networks. Interested students should drop by my office to discuss possible projects.
- Towards Optimal Error-Estimating Codes through the Lens of Fisher Information Analysis [pdf], Nan Hua, Ashwin Lall, Baochun Li, and Jun Xu. In Proceedings of SIGMETRICS, London, UK, 2012.
- Dense Subgraphs on Dynamic Networks [pdf], Atish Das Sarma, Ashwin Lall, Danupon Nanongkai, Amitabh Trehan. In Proceedings of DISC, Salvador, Brazil, 2012.
- Regret-Minimizing Representative Databases [pdf], Danupon Nanongkai, Atish Das Sarma, Ashwin Lall, Richard J. Lipton, and Jim Xu. In Proceedings of the 36th International Conference on Very Large Databases, Singapore, 2010.
- Streaming Pointwise Mutual Information [pdf], Benjamin Van Durme and Ashwin Lall. In Proceedings of the Neural Information Processing Systems Conference, Vancouver, Canada, 2009.
- Data Streaming Algorithms for Estimating Entropy of Network Traffic [pdf], Ashwin Lall, Vyas Sekar, Mitsunori Ogihara, Jun Xu, and Hui Zhang. In Proceedings of ACM SIGMETRICS 2006/IFIP Performance, Saint Malo, France, 2006.
Lew Ludwig joined the Denison faculty in 2002. Prior to this, he had visiting positions at Miami University and Kenyon College. He earned his doctorate at Ohio University under his advisor A. V. Arhangelskii, a Master’s Degree in Mathematics at Miami University and a Master’s in Education from the College of Mount St. Joseph. Dr. Ludwig has taught a variety of classes at Denison including FYS 102, Math 121, Math 122, Math 123, Math 124, Math 231, Math 210, Math 321/322 and Math 400 Knot Theory. He also teaches Math 215 Technically Speaking. In recent years, Dr. Ludwig has adopted the “flip classroom” format where students engage in the material before coming to class. In 2013, he was awarded the Distinguished Teaching Award from the Ohio Section of the Mathematical Association of America.
Selected student research projects:
- Joseph Paat (’11) and Erica Evans (’11), An infinite family of knots whose mosaic number is realized in non-reduced projections, won best presentation at MathFest 2010.
- Joseph Paat (’11) and Jacob Shapiro (’10), Tabulating knot mosaics, won best presentation at JMM 2010 Poster Session.
- Sam Behrend (’09), Linking in straight-edge embeddings of K9, won best presentation at MathFest 2008 and JMM 2009 Poster Session.
- Rachel Grotheer (’08) Linking in straight-edge embeddings of K8, won best presentation at MathFest 2007 and JMM 2008 Poster Session.
- Colleen Hughes (’06) Linking in straight-edge embeddings of K6, won best presentation at MathFest 2004 and JMM 2005 Poster Session.
Dr. Ludwig was trained as a point-set topologist and continues work in this field looking at separation and convergence-type problems. In order to include undergraduates in his work, Dr. Ludwig expanded his research to include knot theory, a branch of topology. Since 2005, Dr. Ludwig has worked with nine undergraduate students on seven different research projects. Combined, his students have won 11 national awards with cash prizes totaling over $1000, for the quality of their work and presentations. Dr. Ludwig is happy to advise summer research students in any area of knot theory. He and his students have been very successful with the two hands-on topics of stick knots and knot mosaics, producing four peer-reviewed publications.
- An infinite family of knots whose mosaic number is realized in non-reduced projections (with Erica Evans (’11) and Joe Paat (’11)), Journal of Knot Theory and its Ramifications, 22:7, 2013
- Linking in straight-edge embeddings of K7 (with Pameila Arbisi (’07)), Journal of Knot Theory and its Ramifications, 19:11, pp. 1431-1447, 2010.
- Dowker Spaces Revisited (with Nyikos and Porter), Tsukuba Journal of Mathematics 34:1, pp. 1-11. 2010
- When graph theory meets knot theory (with Foisy), Contemporary Mathematics 479, pp. 67–85, 2009
May Mei joined the Denison faculty in 2013 after completing her PhD in mathematics at the University of California, Irvine. In addition to teaching a wide variety of courses, Dr. Mei is the faculty advisor for Pi Mu Epsilon, the math honor society. Also, Dr. Mei relishes conversations with aspiring young mathematicians and encourages her students and other math majors to visit her office.
Selected student research projects:
- Asymptotic Spectral Properties of the Schrodinger Operator with Thue-Morse Potential, William Clark (Ohio University), Rachael Kline (St. John Fisher College), Michaela Stone (Louisiana State University), Summer 2013
- On the Spectrum of the Penrose Laplacian, Michael Dairyko (Iowa State University), Christine Hoffman (Smith College), Julie Pattyson (University of St Joseph), Hailee Peck (Millikin University), Summer 2013
- Asymptotic Analysis of the Spectrum of the Discrete Hamiltonian with Period Doubling Potential, Meg Fields (University of North Carolina at Asheville), Tara Hudson (University at Buffalo), Maria Markovich (Shippensburg University), Summer 2013
- Using the Ammann-Beenker Tiling to Model Quasicrystals, Brittany Livsey (Georgetown College), Jason Mifsud (Binghamton University), Francesca Romano (Siena College), Summer 2013
My research interests involve the application of dynamical systems (uniformly hyperbolic, partially hyperbolic, symbolic) to mathematical physics. Specifically, I use dynamical techniques to investigate spectral properties of operators involved in the study of quasicrystals.
I'm also interested in conducting numerical experiments related to mathematical models that describe how an electron passes through quasicrystalline material. This is an area with many possibilities for undergraduate research.
- Tridiagonal substitution Hamiltonians, I. Spectral analysis (with W. Yessen), submitted.
- Spectra of Discrete Schrödinger Operators with Primitive Invertible Substitution Potentials, submitted.
I grew up in Virginia in a small town and received a Ph.D. in Mathematics at the University of Virginia in Charlottesville. After completing my Ph. D. work at Oxford and teaching for two years at The University of California at Irvine, I came to Denison where I have spent the last 12 years. I have a wife, Nancy, and two kids, Joseph (14) and Emily (11). Mathematically, I am interested in operator theory, probability, and statistics. Outside of mathematics, I am interested in Jesus Christ first and foremost. I am also interested in games, history, sports statistics, indie rock, and showing mercy to the poor, lonely, and marginalized.
Selected student research projects:
- Modeling player value in the NBA, Danny Persia, Summer 2013 (awarded a Pi Mu Epsilon Research Presentation Award, Math Fest 2013)
- Metric-linear characterizations of operator algebra structures, Matt Gibson, 2012-2013 (presented at Joint AMS/MAA meetings, 2013)
- Toward a metric-linear characterizations of operator algebras, Nathan Zakhari, 2010-2011 (awarded a research presentation award, Math Fest 2010)
- Toward a classification of n-uniform frames in linear coding theory, Glen Sutula, 2011 (presented at Math Fest 2010)
Recently, I have done research with students in NBA basketball analytics. I try to determine what players are worth, which five man-units play well together, and which coaching strategies are most successful. To do this, I use statistical modeling methods that are commonly used in most real world industries. Hence, research in NBA analytics is an excellent preparation for any career that involves analyzing data to solve problems.
Much of my research is in Functional Analysis and Algebra. More specifically, I study the algebra, geometry and topology of spaces of operators. Operators represent the basic observables of the universe, like energy and momentum. Although my work is theoretical, the problems I solve are motivated by probabilistic questions in Quantum Mechanics. I have had success working with students on such problems. Unlike my basketball analytics projects discussed above, operator theory requires students to be somewhat advanced in their mathematical education. Students who want to pursue a Ph. D. in Mathematics will benefit most from this kind of work.
- A holomorphic characterization of operator algebras (with B. Russo) to appear in Mathematica Scandinavica, 2013
- Metric characterizations II (with D. Blecher) to appear in the Illinois Journal of Mathematics, 2013
- Open projections in operator algebras II: compact projections (with D. Blecher), Studia Mathematica 208, pp. 203-224, 2012
- Open projections in operator algebras I: comparison theory (with D. Blecher). Studia Mathematica 209, pp. 117-150, 2012
- Metric haracterizations of isometries and of unital operator spaces and systems (with D. Blecher). Proceedings of the American Mathematical Society 139, pp. 985-998, 2011
Sarah Rundell grew up in the Boston area, and she did her undergraduate work at Bryn Mawr College, where she earned an A.B. in Mathematics. She received her Ph.D. from the University of Michigan - Ann Arbor under the direction of Phil Hanlon, and she joined the Denison faculty in 2007. Dr. Rundell enjoys teaching a variety of math courses, including Calculus, Combinatorics, Introduction to Proofs, Linear Algebra and Differential Equations, Abstract Algebra, and Operations Research. She is also the faculty advisor to the department's student chapter of the Association of Women in Mathematics. Her community service includes being involved with the Elizabeth Ministry at her parish as well as being a sponsor for the RCIA process. Dr. Rundell also enjoys watching Michigan and Patriots football games, running, cooking, and reading, and she is interested in Ignatian spirituality.
Selected student research projects:
Nathaniel Kell, Investigation of Coloring Complexes in Hypergraphs, Summer 2012.
Mary Kimberly and Beidi Qiang, A Combinatorial Interpretation of a Kostka Matrix Identity, Summer 2010.
Combinatorics is a field of mathematics that deals with the study of discrete structures. At Denison, I teach a course in enumerative combinatorics that covers different methods for counting certain discrete structures, and I am interested in directing student research projects in this field. My research interests lie in algebraic and topological combinatorics, which means that I use algebraic and topological tools to study discrete structures. Recently, I have been interested in the coloring complex and the relationships between the topology of the coloring complex and the chromatic polynomial of the underlying graph, hypergraph, or signed graph.
Hyperoctahedral Eulerian idempotents, Hodge decompositions, and signed graph coloring complexes (with B. Braun), submitted to the Electronic Journal of Combinatorics, 2013
Asymmetric 2-colorings of planar graphs in S^3 and S^2 (with E. Flapan and M. Wyse), submitted to the Journal of Graph Theory, 2013
The coloring complex and cyclic coloring complex of a complete k-uniform hypergraph, Journal of Combinatorial Theory, Series A. 119. no. 5: 1095-1109, 2012
The Hodge structure of the coloring complex of a hypergraph (with J. Long), Discrete Mathematics 311 no. 20: 2164-2173, 2011
The homology of the cyclic coloring complex of a simple graph, Journal of Combinatorial Theory, Series A, 116, no. 3: 595-612, 2009
Michael Westmoreland grew up in America, attending sixteen different schools in Texas, Illinois and Missouri before graduating from high school. He did his undergraduate work at M.I.T. and Rice University, earning a B. A. in Mathematics and Economics from the latter. He received his Ph. D. from the University of Texas - Austin under the direction of David Saltman. He joined the Denison faculty in 1990. Professor Westmoreland enjoys teaching a variety of math courses, including Calculus, Real Analysis, Measure Theory, Probability, Introduction to Proofs, Linear Algebra and Differential Equations, Abstract Algebra, Topology and Graph Theory. He also enjoys watching cooking, reading, and teaching the occasional adult Sunday School class at his local Methodist church.
Selected student research projects:
Entanglement in rational function fields of finite characteristic, Ruijun Ma, 2013.
Multiparty entanglement in finite vector spaces, Yige Li, 2011 - 2012.
Entanglement in Finite Vector spaces, R. J. Singh, 2009 – 2010.
My research focuses on the foundations of quantum mechanics. As this physical theory is understood through its mathematical models (a fancy way of saying no one has an intuitive understanding of quantum mechanics), questions about foundational issues are well suited for attack by mathematical methods. Quite often the approach taken by my collaborators and me involves methods drawn from information theory. One our key results – the classical capacity of quantum channels – is a prime example of the application of such information theoretic methods. This result not only sets bounds for actual physical methods of communication it also provides a physical meaning to the mathematical construct know as “quantum entropy.”
Recently I have conducted recent research with students studying the entanglement structure of finite vector spaces; that is vector space over finite fields. Entanglement is the feature of quantum systems that provides ability for quantum systems to be teleported and for the increased power offered by quantum computing. Entanglement is also the feature of quantum mechanics that caused scientists such as Einstein, Podolsky and Rosen to doubt the ultimate validity of quantum mechanics. Einstein is famous for referring to the “spooky action at a distance” that entanglement leads too. But every prediction made by entanglement based models has so far stood the test of experiment. In finite fields, much of the abstract structure of quantum mechanics is simplified but may of the odd properties of quantum systems remain. These finite systems provide a handy “test bed” for conjectures about entanglement. My students have expanded our knowledge about entanglement in such simple systems. Students undertaking such research learn the fundamentals of quantum mechanics and finite field theory.
With B. Schumacher, “Reverend Bayes takes the Unexpected Examination”, Math Horizons, (September, 2008).
With B. Schumacher, “Isolation and information flow in quantum dynamics”, Foundations of Physics, (May, 2012).
With B. Schumacher, “Modal Quantum Theory”, Foundations of Physics, (May, 2012).
With B. Schumacher, “Possibility, probability, and entanglement: Non-contextuality in modal quantum mechanics”, Foundations of Probability and Physics – 6, American Institute of Physics; Melville, New York (2012).
With B. Schumacher, Quantum Processes, Systems and Information, Cambridge University Press; Cambridge, U.K. (2011).