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Associate Professor

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(205) 934-8557
University Hall 4008

Research and Teaching Interests: Probability theory, Quantum spin systems

Office Hours: M/W 4:30 - 5:20 p.m.; and by appointment

Education:

  • Ph.D., University of California Davis, The Low Spectrum of the XXZ Model

I received my Bachelor's degree in mathematics at UC Berkeley and my Ph.D. from UC Davis. I held temporary teaching/research positions at Princeton, McGill in Montreal (Canada), and UCLA, and had a permanent faculty position at University of Rochester in upstate New York before finally settling down at UAB.

I have taught courses with a variety of instructional methods, including regularly teaching a two-semester course using inquiry based learning (IBL). In IBL courses in mathematics, students present all the material, especially proofs of theorems, and the instructor spends all their time as an audience member. I also frequently teach and use Mathlab as an element in courses such as Mathematical Statistics, Mathematical Finance, and Advanced Probability. In such classes, computing is one of several useful tools for gaining mathematical understanding and insight.

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Research Interests

Mathematical physics is the study of physical systems using the methods of mathematics, especially rigorous proofs. It is the only fool-proof way to resolve discrepancies or controversies among physicists. A notable example is Peierls's proof in the mid 20th century that phase transitions can occur in physical systems using the set up of theoretical statistical mechanics. This fact was previously doubted by about half the physicists at a major conference. This is the high ideal mathematical physicists aspire to. Probability theory is a necessary part of mathematical physics, just as it is a component of quantum mechanics. I work on mathematics related to quantum spin systems as well as on spin glasses and other topics in probability theory such as random matrices and random permutations.

Recent Courses

  • MA 440-441/540-541: Advanced Calculus
  • MA 484: Mathematical Finance
  • MA 486: Mathematical Statistics
  • MA 687: Advanced Probability
  • EGR 265: Mathematics for Engineers

Select Publications

  • Meg Walters and Shannon Starr. "A Note on Mixed Matrix Moments for the Complex Ginibre Ensemble." J. Math. Phys. (2015) 56, 013301.
  • Nicholas Crawford, Stephen Ng, and Shannon Starr. "Emptiness Formation Probability." Commun. Math. Phys. (2016) 345, 881-922.
  • Carl Mueller and Shannon Starr. "The Length of the Longest Increasing Subsequence of a Random Mallows Permutation." J. Theoret. Probab. (2013) 26, 514–40.
  • Ang Wei, Brigitta Vermesi, and Shannon Starr. "About Thinning Invariant Partition Structures." J. Statist. Phys. (2012) 148, 325–44.
  • Pierluigi Contucci, Sander Dommers, Cristian Giardinà, and Shannon Starr. "Antiferromagnetic Potts model on the Erdos-Renyi random graph." Commun. Math. Phys. (2013) 323, 517–54.
  • Shannon Starr. "Thermodynamic Limit for the Mallows Model on Sn." J. Math. Phys. (2009) 50.
  • Marek Biskup, Lincoln Chayes, and S. Starr. "Quantum spin systems at positive temperature." Commun. Math. Phys. (2007) 69, 611-57.
  • Bruno Nachtergaele and Shannon Starr. "A Ferromagnetic Lieb-Mattis Theorem." Phys. Rev. Lett. (2005) 94, 057206.
  • Michael Aizenman, Robert Sims, and S.L. Starr. "An extended variational principle for the SK Spin-Glass model." Phys. Rev. B (2003) 68, 214403.

Academic Distinctions & Professional Memberships

  • Member of the International Association of Mathematical Physicists