This course is a special version of Marine Biology (ZOOL 345) co-taught by
Amy Downing and myself.
The course covers both physical and biological features of major marine habitats,
as well as the ecology and physiology of representative animals. The course will emphasize coral
reef and mangrove habitats that will be explored during a travel component to St. John USVI in
the Caribbean. Mathematical models of physical and biological systems will be presented and
discussed in association with the topics. Students will design research projects in
which they will build a mathematical model and then collect relevant data on the field trip that will
allow them to parameterize their model. We will also discuss human interactions with the marine
environment including human impacts on coral reefs, fisheries, marine mammals and coastal
ecosystems. Prerequisites: BOMI/ZOOL 122 (Organisms and their environment) and MATH 110 (Calculus I).
See the link above for the course syllabus.
This course examines climate from a mathematical point of view focusing on how various climate
processes can be described using mathematical models. For example: box models of ocean and atmospheric transport,
radiative-convective atmospheric models, one dimensional Budyko-Sellers type models,
models of glaciers and climate/glacier interaction. Basic notions of meteorology will be introduced/derived. Other topics include: numerical and analytic
methods of solving systems of ODEs, analysis of feedbacks, stability of equilibria. Students will build and run models using software such as Mathematica, MATLab, and R.
Each student will complete an independent research project. Course concludes in May with a 10-12 day trip to Alaska to study katabatic flow
on valley glaciers and interact with modelers at the University of Alaska, Fairbanks. See the link above for course webpage.
Introduction to Mathematical Biology (work in progress)
Advancement in the biological sciences increasingly relies on mathematical and computational techniques. From proteins and genes to organisms and ecosystems, biologists are finding more and more that modern problems in biology require quantitative thinking in addition to knowledge of traditional biological principles. This course introduces mathematical and numerical techniques as applied to problems in the biological sciences. Mathematical methods include discrete and continuous modeling, limiting behavior, stability analysis, matrices and spectral methods, phase plane analysis, and numerical simulation. Biological applications are drawn from a variety of topics, including population dynamics, genetics, ecology, epidemiology, and neurobiology.
Student Seminar, Fall 2010, 2011
This course is intended to be a true student seminar in that the topic of study is chosen by the students (in consultation with the instructor) and it is the students themselves who lecture to each other on the material. Essentially, this course tries to make what is a common occurrence in graduate school into a successful experience for undergraduates. In addition, a writing credit will be given to those students who complete an independent research project including writing a mathematical paper in LaTeX (the standard typesetting language used by mathematicians).
Past topics have included Differential Geometry (using Thorpe) and Graph Theory (using Bollobas).
Opportunities for undergraduates interested in math and its applications:
The Young Mathematicians Conference (YMC) is the premier national conference for undergraduate student research in mathematics. It is held every August at the Ohio State University and provides the opportunity for about 70 undergraduates to present their research and interact with their peers. Plenary talks are also given by top research mathematicians (e.g., Terence Tao, Peter Sarnak, John Conway, Peter Shor, etc.).
I received my Ph.D. from the University of Chicago in 2007. My thesis
was on the algebraic geometry of nilpotent orbits in semi-simple Lie
Algebras. I received an M.S. from The Ohio State University in 2001.
My masters thesis was on representations of braid groups. My undergraduate
work was done at the University of Alaska, Anchorage.
I am interested in topics in the intersection of representation theory, braid groups, and quantum algebras. I also have interests in topology, knot theory, mathematical biology, mathematical climate models, and I enjoy thinking about the ways in which mathematics appears in popular culture and non-mathematical texts.
Challenges in promoting undergraduate research
in the mathematical sciences. With Feryal Alayont, Yuliya Babenko, and Zsuzsanna Szaniszlo. Involve, 7:3 (2014) 265-271. (web)
Polar Amplification: Is Atmospheric Heat Transport Important? With Vladimir Alexeev. Climate Dynamics, 41:2 (2013) 533-547. (pdf)(web)
Modeling the Impact of Afforestation on Global Climate: A 2-box EBM. With Sriharsha Masabathula. J. Env. Stat. 4:12 (2013). (pdf)(web)
Topologies of Identity in Serial Experiments Lain. Mechademia 7: Lines of Sight, Ed. Frenchy Lunning, Univ. of Minnesota Press (2012) 191-201.
Isaac Kochman, Investigations Into the Symmetric Group, 2018. (pdf)
Khanh Q. Le, Specializations of the Lawrence Representations of the Braid
Groups at Roots of Unity, 2016. (pdf)
Nam Tran Hoang, A Recursive Formulation for the Rank-Sum Statistic used to detect Genomic Copy Number Variation, 2016. (pdf)
is a well known fact - attested to by J. Peter May, no less - that
the entering class of 2001 is the best class the University of Chicago
Math Department has ever known. It goes without saying, then, that
the Beer Skits of 2003 may rightly be called the Best Beer Skits Ever.
is my privilege, then, to be the sole custodian of the Eternal
Electronic Monument to Beer Skits '03. This is quite a responsibility,
as you can imagine, and I take it very seriously. I think I would
even put this on my CV if more people knew about Beer Skits. Thankfully,
you a second year math student at the U of C? If so, then please recall
these famous words of Andre Weil: "No beer skits, no degree!"
I am interested in topics in the intersection of representation theory, braid groups, and quantum algebras. I also have interests in topology, knot theory, mathematical biology, mathematical climate models, and I enjoy thinking about the ways in which mathematics appears in nonmathematical texts.
The Krammer-Lawrence-Bigelow Representation of the Braid Groups via U_q(sl_2). With Thomas Kerler. Adv. Math. 228 (2011) pp. 1689-1717. (arXiv)
"It Really Tied the Room Together": Axiomatics, Formal Systems, and Incompleteness in The Big Lebowski. To appear as The Big Lebowski and Mathematical Logic in The Big Lebowski and Philosophy, Ed. Peter Fosl, Wiley-Blackwell, 2012.
Topologies of Identity in Serial Experiments Lain. To appear in Mechademia 7: Lines of Sight Ed. Frenchy Lunning, Univ. of Minnesota Press, 2012.
Bethe Ansantz for Central Arrangements of Hyperplanes. (pdf)
Symplectic Manifolds, Geometric Quantization, and Unitary Representations of Lie Groups. Chicago 2nd year Topic. (pdf)
Braid Group Representations. OSU Masters Thesis. (pdf)