The Directed Reading Program (DRP) at UIC is a program in which undergraduate students are paired with graduate student mentors and pursue independent reading projects. The presentation session for the Fall 2024 iteration of the DRP will be held on Friday, December 6 from 11AM to 2PM in SEO 636. The schedule for the presentation session is as follows:
11AM:
The application for the Spring 2025 iteration of the DRP will be available on this page on January 13. Eligibility is limited to undergraduate students at UIC. Students may apply to receive one college credit for participating in the DRP as well. Students who wish to apply for the college credit must apply by January 20. All applications received by January 20 will be considered equally, regardless of whether the student is applying for the college credit. The deadline for applying is January 24. Eligibility is limited to undergraduate students at UIC. The timeline for Spring 2025 iteration of the DRP will be as follows:
Undergraduate students interested in a first experience with mathematics outside the classroom, as well as undergraduate students who may have undergone challenges throughout their journey with mathematics as a result of their identity or life circumstances, are highly encouraged to apply.
The current list of mentors for the DRP is as follows:
Darius Alizadeh
Julian Benali
Lisa Cenek
Nick Christo
Karoline Dubin
Michael Gintz
Shin Wook Kim
Katie Kruzan
Sacha L'Heveder
Clay Mizgerd
Abhijeet Mulgund
Amelia Pompilio
Theo Sandstrom
Jaegeon Shin
Duan Tu
Jennifer Vaccaro
Jagerynn Verano
Ping Wan
Information regarding older presentation sessions can be found below:
This program is hosted by the UIC student organization Symbols of Inclusion and co-organized by Nick Christo and Michael Gintz. Questions regarding the program can be directed to Michael Gintz at mgintz2@uic.edu.
11AM:
A summary of Gödel's Incompleteness Theorems
Michael Schmidt, mentored by Julian Benali
Abstract: We gave a brief history and explanation of Gödel's Incompleteness Theorems. We'll give an example of Gödel numbering and the proof idea for Gödel's theorems.
TBD
Diana Dobrovolsky, mentored by Chirag Singhal
Geometric Group Theory and the Milnor-Schwarz Lemma
Noah Zabelka, mentored by Darius Alizadeh
Abstract: Assuming no familiarity with geometric group theory (though some knowledge on groups and metric spaces will be very helpful), we will be taking a crash course from a standard introduction to one of its most fundamental results: the Milnor-Schwarz Lemma. This will include brief descriptions from the geometric properties of a group, up to quasi-isometries and the Milnor-Schwarz Lemma.
Structured Sets, Categories, and Certain Applications
Caleb Williams, mentored by Vignesh Jagathese
Abstract: We review rigorous definitions of sets and classes, ordered pairs, relations, mappings of sets, structured sets such as groups, topological spaces, and sigma-algebras, and properties of compositions of maps between them that preserve the structure that these sets are equipped with. We introduce the definition of a category and introduce basic examples of categories.
12PM:Michael Schmidt, mentored by Julian Benali
Abstract: We gave a brief history and explanation of Gödel's Incompleteness Theorems. We'll give an example of Gödel numbering and the proof idea for Gödel's theorems.
TBD
Diana Dobrovolsky, mentored by Chirag Singhal
Geometric Group Theory and the Milnor-Schwarz Lemma
Noah Zabelka, mentored by Darius Alizadeh
Abstract: Assuming no familiarity with geometric group theory (though some knowledge on groups and metric spaces will be very helpful), we will be taking a crash course from a standard introduction to one of its most fundamental results: the Milnor-Schwarz Lemma. This will include brief descriptions from the geometric properties of a group, up to quasi-isometries and the Milnor-Schwarz Lemma.
Structured Sets, Categories, and Certain Applications
Caleb Williams, mentored by Vignesh Jagathese
Abstract: We review rigorous definitions of sets and classes, ordered pairs, relations, mappings of sets, structured sets such as groups, topological spaces, and sigma-algebras, and properties of compositions of maps between them that preserve the structure that these sets are equipped with. We introduce the definition of a category and introduce basic examples of categories.
(Weak) Law of Large Numbers
Sebastian Tous, mentored by Nick Christo
Abstract: The Weak Law of Large Numbers, a cornerstone of probability theory, states that the sample mean of independent, identically distributed random variables converges in probability to the true mean as the sample size grows. This presentation covers the foundational theory required to understand this result, its extension to the Strong Law of Large Numbers, and the key differences between the two. We then examine its application to the St. Petersburg paradox, a coin-flipping game with infinite expected value, to examine how much one should rationally wager to play.
An application of the Borel-Cantelli lemma
Albert Arias, mentored by Shin Kim
Abstract: In this presentation we explore how the Borel-Cantelli lemma can be used to show that the largest run of heads in n independent tosses of a fair coin will will almost surely grow like log(n).
Introduction to Differential Geometry
Gabriel R. D. Ruiz, mentored by Jaegeon Shin
Abstract: This presentation will contain a review of curvature and torsion, cover Fernet Frame which is local theory, and then move to global theory. We then will look at the isoperimetric inequality.
1PM:Sebastian Tous, mentored by Nick Christo
Abstract: The Weak Law of Large Numbers, a cornerstone of probability theory, states that the sample mean of independent, identically distributed random variables converges in probability to the true mean as the sample size grows. This presentation covers the foundational theory required to understand this result, its extension to the Strong Law of Large Numbers, and the key differences between the two. We then examine its application to the St. Petersburg paradox, a coin-flipping game with infinite expected value, to examine how much one should rationally wager to play.
An application of the Borel-Cantelli lemma
Albert Arias, mentored by Shin Kim
Abstract: In this presentation we explore how the Borel-Cantelli lemma can be used to show that the largest run of heads in n independent tosses of a fair coin will will almost surely grow like log(n).
Introduction to Differential Geometry
Gabriel R. D. Ruiz, mentored by Jaegeon Shin
Abstract: This presentation will contain a review of curvature and torsion, cover Fernet Frame which is local theory, and then move to global theory. We then will look at the isoperimetric inequality.
Information Theory: Huffman Codes
Harry Alvarado, mentored by Abhijeet Mulgund
Abstract: Introduce the mathematical ideas of encoding and ultimately prove that Huffman codes are optimal encodings
Differential Privacy and its Real Life Applications
Qiming Li, mentored by Duan Tu
Abstract: TBD
Chaotic Cellular Automata Image Compression
Sam Stuckey, mentored by Karoline Dubin
Abstract: Cellular automata cover the breadth of elementary and very complex systems and have been rashly relegated to the theory of computing and modeling dynamical systems. But, they can be so much more than that! Using the variance in CA rules, people came up with ways to use CA in practical ways, including image compression, which will be the focus of this talk.
Wanna solve Hilbert's tenth? think again
Bill Shepelak, mentored by Katie Kruzan
Abstract: Some problems are not solvable through computation. Computability theory gives us the tools to show why this is the case with certain types of problems. Using results from computability theory we are able to show through a technique called reduction that no decidable algorithm exists as a solution to Hilbert's 10th problem regarding finding solutions to Diophantine equations with more than one independent variable.
Harry Alvarado, mentored by Abhijeet Mulgund
Abstract: Introduce the mathematical ideas of encoding and ultimately prove that Huffman codes are optimal encodings
Differential Privacy and its Real Life Applications
Qiming Li, mentored by Duan Tu
Abstract: TBD
Chaotic Cellular Automata Image Compression
Sam Stuckey, mentored by Karoline Dubin
Abstract: Cellular automata cover the breadth of elementary and very complex systems and have been rashly relegated to the theory of computing and modeling dynamical systems. But, they can be so much more than that! Using the variance in CA rules, people came up with ways to use CA in practical ways, including image compression, which will be the focus of this talk.
Wanna solve Hilbert's tenth? think again
Bill Shepelak, mentored by Katie Kruzan
Abstract: Some problems are not solvable through computation. Computability theory gives us the tools to show why this is the case with certain types of problems. Using results from computability theory we are able to show through a technique called reduction that no decidable algorithm exists as a solution to Hilbert's 10th problem regarding finding solutions to Diophantine equations with more than one independent variable.
The application for the Spring 2025 iteration of the DRP will be available on this page on January 13. Eligibility is limited to undergraduate students at UIC. Students may apply to receive one college credit for participating in the DRP as well. Students who wish to apply for the college credit must apply by January 20. All applications received by January 20 will be considered equally, regardless of whether the student is applying for the college credit. The deadline for applying is January 24. Eligibility is limited to undergraduate students at UIC. The timeline for Spring 2025 iteration of the DRP will be as follows:
- January 27: Program begins, students are paired with mentors
- February 3: Project proposals due
- March 14: Project updates due
- April 18: Titles and abstracts due
- May 2: Presentations
Undergraduate students interested in a first experience with mathematics outside the classroom, as well as undergraduate students who may have undergone challenges throughout their journey with mathematics as a result of their identity or life circumstances, are highly encouraged to apply.
The current list of mentors for the DRP is as follows:
Darius Alizadeh
Darius Alizadeh is a 5th 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!
Julian Benali
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
Lisa Cenek is a 2nd 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
Nick Christo is a 5th-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.
Karoline Dubin
Karoline Dubin is a 5th-year PhD student interested in probability theory, statistical physics, and computer science. She is interested in topics of math with physical motivation and algorithmic applications, and is excited to explore such topics with undergrads.
Michael Gintz
Michael Gintz is a third-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.
Shin Wook Kim
Shin Kim is a 4th-year PhD student studying Complex Geometry. He is interested in reading with undergraduate students on any topic that they are interested in.
Katie Kruzan
Katie Kruzan is a 3rd year 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
Sacha L'Heveder is a 2nd-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.
Clay Mizgerd
Clay Mizgerd is a 3rd-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
Abhijeet Mulgund is a 4th 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.
Amelia Pompilio
Amy Pompilio is a 6th-year PhD student studying metric and projective geometry. She is most interested in reading papers having to do with Hilbert geometries and books that introduce hyperbolic geometry to new readers.
Theo Sandstrom
Theo Sandstrom is a 2nd-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.
Jaegeon Shin
Jaegeon is a fifth-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!
Duan Tu
Duan Tu is a 5th year PhD student studying Mathematical Computer Science. Her current research focuses on machine learning theory, but her interests also involve probability and discrete math in general. Through the Directed Reading Program, she wants to help undergraduate students break the seemingly steep barrier to advanced math and math research. She is excited to learn something new together with the student!
Jennifer Vaccaro
Jennifer Vaccaro is a 5th-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."
Jagerynn Verano
Jagerynn is a fifth year PhD student. She does geometric group theory and is interested in reading on topics like algebraic topology, geometry and group theory. She is also open to other recommendations!
Ping Wan
Ping Wan is a 5th-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.
Information regarding older presentation sessions can be found below:
This program is hosted by the UIC student organization Symbols of Inclusion and co-organized by Nick Christo and Michael Gintz. Questions regarding the program can be directed to Michael Gintz at mgintz2@uic.edu.