Cam McLeman

Cam McLeman

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My research interests lie in the application of mathematical tools to machine learning models, e.g., using tools from graph theory and stochastic processes to study graphical neural networks, and conversely, the application of artificial intelligence to mathematical proofs, e.g., automated theorem-proving and theorem-generation. With IDEAS, I also work to use more standard applications of machine learning models to solve problems for groups who traditionally lack access to data science expertise.

My doctoral training was in algebraic number theory, and one of the boasts of number theory is that you are required to use tools from every discipline in mathematics to understand all of its facets. This brought me in contact with graph theory both in the abstract and in the applied setting of Markov chains and stochastic processes, and using these ideas to model evolutions of systems in natural settings. Most recently, the dynamic updating of stochastic processes on graphs is very similar in spirit to the training of many models of neural networks, and exploring the symbiosis between these two sets of ideas has been a driver of my recent research.

In IDEAS, we are excited about taking the reams of student and faculty expertise and research at the University of Michigan and using it “for the people” — finding ways of furthering the goals of small businesses or local community groups that do not have the resources to have a data scientist on staff. On the research front, I personally am very excited to see how the study of mathematics evolves as generative AI models meet formal theorem-proving systems.

Mahesh Agarwal

Mahesh Agarwal

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Prof. Agarwal’s is primarily interested in number theory, in particular in p-adic L-functions, Bloch-Kato conjecture and automorphic forms. His secondary research interests are polynomials, geometry and math education, Machine Learning, and healthcare analytics.

Jeffrey C. Lagarias

Jeffrey C. Lagarias

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Jeffrey C. Lagarias is theĀ Harold Mead Stark Collegiate Professor of Mathematics in the College of Literature, Science, and the Arts at the University of Michigan, Ann Arbor.

Prof. Lagarias’ research interests are diverse. His initial training was in analytic and algebraic number theory. After receiving his PhD in 1974, he worked at Bell Laboratories and AT &T Labs until 2003, on problems in many pure and applied fields. Besides number theory, Prof. Lagarias has made contributions in harmonic analysis (wavelets and fractals), mathematical optimization (interior point methods), discrete geometry (tilings and quasicrystals), ergodic theory, low-dimensional topology (complexity of unknotting), and theoretical computer science.

At Michigan Prof. Lagarias has been active in the number theory group over the last few years, with additional work in other fields. His last 25 postings on the arXiv were in: Number Theory (16), Dynamical Systems (3), Classical Analysis and ODE?s (3), Metric Geometry (1), Optimization and Control (1), Spectral Theory (1). His doctoral students typically work on their own topics. Some have worked in topics in number theory: integer factorial ratios, character sum estimates, Diophantine equations with two separated variables; Others have worked in topics in discrete geometry: packings of regular tetrahedra, rigidity of circle configurations.

 


Research Highlights