Mentors

Darius Alizadeh is a 6th year PhD student who studies groups through their actions on geometric objects, aka geometric group theory. Any topic where you can draw pictures and think in shapes is a good fit for him, including manifolds, algebraic topology, and more. He would love to explore some interesting topic outside the standard curriculum. Math is a big world to explore!

Hassan Babaei is a 5th year PhD student specializing in analysis and partial differential equations (PDEs). His research focuses on understanding behaviors of certain kinds of PDEs with applications in physics. Hassan enjoys working with undergraduate students on exploring interesting questions in analysis and PDEs, and reading research papers. He aims to help mentees develop both strong technical skills and a deep conceptual understanding of the material. 

Julian Benali is a PhD student studying commutative algebra, though he also has interests in logic, topology, and category theory. Julian is looking to work with an experienced undergraduate on a reading project in pure math. The direction is up to the student, but potential topics could include tight closure theory, the chain conjecture, recent developments in intuitionist math, or applications of topos theory.

Lisa Cenek is a 3rd year PhD student. During undergrad, she focused on graph theory, especially combinatorial optimization problems. Graph theory is an exciting area of math with lots of pretty drawings and interesting topics to read about. Lisa is open to working with students coming from any level of mathematics background (no prior experience with graph theory required). She also enjoys other computer science adjacent areas of math such as algorithms and logic, and she is looking forward to getting to work with a student on a topic they are interested in learning about. 

Nick Christo is a 6th-year PhD candidate studying probability, combinatorics, and statistical physics. I have in mind reading through a few chapters of a textbook (e.g., graph theory, probability texts), reading through papers is also an option on any MCS related topic. Reading independently can be a challenging experience that one has to almost learn how to do and would be happy to help make that an easier experience.

André is a third year PhD student studying number theory, elliptic curves, and arithmetic geometry. This involves understanding the symmetries of algebraic numbers and how they interplay with geometric objects. He would be happy to work with a student on anything of a number-theoretic or algebraic nature. 

Michael Gintz is a fourth-year PhD student studying commutative algebra and algebraic geometry. He'd be happy to introduce students to any number of topics related in whole or in part to either of these fields, and would be most interested to go through a textbook at the student's level to introduce them to a topic.

Vignesh Jagathese is a 5th year PhD student studying Commutative Algebra and Algebraic Geometry. Vignesh likes to use algebraic formalism to encode and understand singularities, or how "bad" a given point or region in a space is, and would thoroughly enjoy working with a UIC undergraduate on such topics. Algebra is widely applied in many fields of mathematics, so there are a lot of different topics to study! Vignesh, for instance, also likes thinking about other applications of commutative algebra such as number theory, arithmetic geometry, or just algebra for its own sake. Ultimately, though, he is happy to mentor undergraduate students and guide them towards papers covering topics that they have interest in.

Katie Kruzan is a 4thyear PhD student studying Mathematical Computer Science with particular interest in Algorithms and Graph Theory. She is interested in reading papers//texts with undergraduate students on topics related to their interest, and also help them learn the skills around getting the most bang-for-the-buck around reading academic texts.

Sacha L'Heveder is a 3rd-year PhD student studying group theory and dynamics. He has familiarity with Geometric Group Theory (fun with shapes), Measured Group Theory (fun with measures), Functional Analysis (fun with functions), and Dynamics (fun, but do it a lot of times). He looks forward to working with an undergraduate on a reading around a topic of their interest.

Michael Lange is a third year PhD student working in Model Theory. He is most interested in mathematical logic and also enjoys algebra. He is open to students' suggestions on a project if they have them; otherwise, he would recommend something of the form "Intro to [whatever subject you think sounds coolest]", aiming to cover the proof and key applications / examples of some fundamental theorem from that subject. 

Dane is a second year PhD student studying algebraic geometry. His interests though are broad enough to overlap the interest of most motivated students. Those finding their interests piqued especially in algebra or complex analysis would be an especially good match, but this is by no means an exhaustive list. 

Clay Mizgerd is a 4th-year PhD student working in probability and combinatorics. In addition to these fields, he especially enjoys number theory, and has a broad background in analysis and algebra. He is happy to read on any field of pure math, and looking forward to learning some new math together.

Abhijeet Mulgund is a 5th year PhD student studying machine learning, information theory, and complexity theory. He studies applications of deep learning to error-correcting codes. He is interested in reading on topics related to complexity theory, machine learning, or probability. These fields form a bridge between applied and pure math, which can lead to some very interesting problems.

Theo Sandstrom is a 3rd-year PhD student primarily studying commutative algebra and algebraic geometry, but with broad interest across mathematics (particularly in topics with geometric flavor). He is happy to work with undergraduates on any topic in this vast realm. Possible topics include: an introduction to X, where X in {algebraic geometry, commutative algebra, homological algebra}; elliptic curves; proof assistants (e.g., Lean, Coq, Agda); algebraic topology; knot theory; foliation theory; p-adic analysis.

Xiaoning Shi is a 3rd-year PhD student studying stochastic analysis, with broad interests in probability, analysis, and partial differential equations. She is happy to work with undergraduates on topics related to probability, stochastic processes, stochastic differential equations, or analysis more generally. She looks forward to exploring a topic of the student's interest. 

Jaegeon is a sixth-year PhD student studying complex geometry, advised by Professor Julius Ross. Complex geometry is a mix of algebra and complex analysis, using techniques from both disciplines to solve geometric problems. He is very passionate about teaching and mentoring students who want to learn more about math beyond the textbooks. Learning math is never easy, but it can be very fun and rewarding with a mentor!

Anh Tran is a 4th-year PhD student studying Algebraic Geometry. His focus is Hodge Theory, which also involves some complex differential geometry and topology. He is most interested in going through a book on any of those topics, but both (the topic and the choice of text) are negotiable. 

Jennifer Vaccaro is a 6th-year PhD student studying hyperbolic geometry, specifically representations of hyperbolic triangle reflection groups. However, she comes from an engineering background, and would love to work with either a math major or a non-math major on a geometry/topology reading project. Possible texts include "The Knot Book" or "Office Hours with a Geometric Group Theorist." 

Edward Varvak is a fourth year PhD student studying algebraic geometry. He's also passionate about differential geometry, algebraic topology, arithmetic geometry, and representation theory. He'd enjoy working though a textbook of any geometric flavor, as well as guiding undergraduate students towards being able to learn math independently! 

Jagerynn is a sixth year phd student in geometry. She is passionate about antiracism and immigration reform.

Ping Wan is a 6th-year PhD student studying Geometric Group Theory. They spend most of their research time drawing triangles, pentagons, or random curves. They are interested in reading papers or surveys with undergraduate students on topics about hyperbolic spaces and/or infinite groups.

Xiaotong (Dawson) Yang is a 3rd-year PhD student interested in partial differential equations. He is interested in meeting undergraduates and reading math on analysis and beyond.