# Research Tutorial Groups (RTGs)

“Research Tutorial Groups” introduce graduate students to mathematical research at the end of the first year and beginning of the second year, typically well in advance of formal dissertation research. In the spring of the first year, students listen to short lecture series on topics of current interest (usually three or four series of three or four lectures, one hour per week). In the following fall, students choose one of the topics and work on a research problem with the sponsoring faculty member and a small group of fellow students. The spring lecture series is one credit hour while the fall research group is three credit hours.

## Current RTGs (Wednesdays, 4 pm, Math 501)

• Jan 15: L-functions, special values and positivity (Hang Xue) (Host Dan Lewis)

• Jan 22: Inverse problems arising in biomedical imaging (Leonid Kunyansky) (Host Maximilian Rezek) This is a special joint session with Applied Math.

• Jan 29: Stochastic vesicle dynamics in synaptic transmission (Calvin Zhang-Molina) (Host Rebecca Jarnutowski)

• Feb: 5: Integrable systems in mechanics and geometry (Anton Izosimov) (Host Justin Perkins-Ollila)

• Feb: 12: On some random' directions (Sunder Sethuraman) (Host Evan Forletta) This is a special joint session with Applied Math.

• Feb: 19: Geometry and Topology in the "real world" (Shankar Venkataramani) (Host Zhixuan Zhang) This is a special joint session with Applied Math.

• Feb 26: Qualitative aspects of evolution PDE (Chris Henderson) (Host Duncan Bennett) This is a special joint session with Applied Math.

• Mar 4: Moduli Spaces in Algebraic Geometry (Yi Hu) (Host Zhixuan Zhang)

• Mar 18: What is spectral geometry (Lennie Friedlander) (Host Dan Lewis)

• Mar 25: What is mathematics education research? Some examples from K to college level (Marta Civil) (Host Conner Hatton)

• Apr 1: Moonshine (Christoph Keller) (Host Justin Perkins-Ollila)

• Apr 8: Patterns in Nature (Alan Newell) (Host William Gammel) This is a special joint session with Applied Math.

• Apr 15: Statistics and Machine Learning (Helen Zhang) (Host Tugce Koc)

• Apr 22: Revisiting Quadratic Approximations (Ibrahim Fatkullin) (Host Sarah Luca)This is a special joint session with Applied Math.

• Apr 29: Free Boundary Problems (Sunhi Choi) (Host Gaurish Korpal)

• May 6: A mysterious family of elementary combinatorial identities (Doug Pickrell) (Host Rebecca Jarnutowski)

## Recent RTGs

### 2018

• Jan 16: Mathematics in the era of Big Data (Marek Rychlik)

• Jan 23: Interpretable & Tractable Machine Learning for Natural and Engineering Sciences (Misha Chertkov) This is a special joint session with Applied Math.

• Jan 30: Geodesics in geometry and physics (Anton Izosimov)

• Feb 6: Locality in Quantum Spin Systems (Bob Sims) This is a special joint session with Applied Math.

• Feb 13: Conformal Welding (Doug Pickrell)

• Feb 20: NO LECTURE

• Feb 27: NO LECTURE

• Mar 13: Langlands correspondences and beyond (Hang Xue)

• Mar 20: Lattices and Sphere Packings (Christoph Keller)

• Mar 27: Modularity and Moduli spaces (Brandon Levin)

• Apr 3: NO LECTURE

• Apr 10: Quantum mechanics in the presence of disorder (Janek Wehr) This is a special joint session with Applied Math.

• Apr 17: (Ibrahim Fatkullin) This is a special joint session with Applied Math.

• Apr 24: (Klaus Lux)

• May 1: (Sunhi Choi)

### 2018

• Jan 17: What is it like to do research in Mathematical Biology? (Calvin Zhang) This is a special joint session with Applied Math and will be in Math 501.

• Jan 24: Introduction to integrable systems (Anton Izosimov)

• Jan 31: Distinction problems (Hang Xue)

• Feb 7: Limit shapes for Gibbs ensembles of partitions (Ibrahim Fatkullin)

• Feb 14: Singular limits: Analysis in the "real world" (Shankar Venkataramani) This is a special joint session with Applied Math and will be in Math 501.

• Feb 21: What is research in mathematics education? (Marta Civil)

• Feb 28: Nonlinear Fourier Analysis (Doug Pickrell)

• Mar 14: Rebecca McGraw

• Mar 21: Critical phenomena and universality in some probability models (Tom Kennedy)

• Mar 28: An introduction to statistical research (Ning Hao)

• Apr 4: Moonshine (Christoph Keller)

• Apr 11: An Introduction to Computational Group Theory (Klaus Lux)

• Apr 18: CANCELLED

• Apr 25: Localized pattern formation (Karl Glasner) This is a special joint session with Applied Math and will be in Math 501.

• May 2: Some problems in Data Science (David Glickenstein) This is a special joint session with Applied Math and will be in Math 501.

### 2017

• Jan 25: Homeomorphisms of a Circle and Factorization (Doug Pickrell)

• Feb 1: Restriction Problems in Representation Theory and Number Theory (Hang Xue)

• Feb 8: Let Us Make Noise, Be Late and Have Fun (Janek Wehr)

• Feb 15: Research in Mathematics Education (Rebecca McGraw)

• Feb 22: Mathematics of Instantons and String Theory (Sergey Cherkis)

• Mar 1: Target Waves in Reaction Diffusion Systems and Arrays of Oscillators (Gabriela Jaramillo)

• Mar 8: (Yi Hu)

• Mar 29: An algebraist and a numerical analyst walk into a bar… (Andrew Gillette) This is a special joint session with Applied Math and will be in Social Sciences 118.

• Apr 12: Transportation network approaches for forecasting the spread of mosquito-borne diseases (Joceline Lega)

• Apr 19: Flows of polygons, graphs, and curves (David Glickenstein) This is a special joint session with Applied Math and will be in Social Sciences 118.

• Apr 26: Self-assembled patterns and materials (Karl Glasner) This is a special joint session with Applied Math and will be in Social Sciences 118.

• May 3: An Introduction to Computational Group Theory (Klaus Lux)

### 2016

• Jan 27: An Introduction to Research in Finite Element Exterior Calculus (Andrew Gillette) This will be a special joint session with Applied Math and will be room 501.

• Feb 3, 10 & 17: Design, analysis and application of Monte Carlo sampling methods (Matthias Morzfeld) February 17th will be a special joint session with Applied Math and will be in room 501.

•Feb 24 & Mar 3: Information and Coding (Marek Rychlik)

• Mar 23 & 30: Students’ Justifications for the Temporal Order of Delta and Epsilon in the Formal Definition of a Limit (Aditya Adiredja)

• April 6 & 13: Diffusion: From experiments to geometry (Janek Wehr)

### 2015

- Jan 21, 28 & Feb. 4: Universal and Isoperimetric Inequalities for Eigenvalues of Elliptic Operators (Lotfi Hermi)
- Feb 11, 18, 25 & March 4, 11: "
*Optimization, geometry, and numerical analysis: An approach to modeling capillary origami* - Joceline Lega
*Searching for the Minimum of a Functional* - David Glickenstein
*Geometric Manifolds via Triangulation* - Nick Brubaker
*Mathematics and Modeling of Elasto-capillary System* - Andrew Gillette
*A Brief Introduction to Splines on Triangulations* - March 18: No lecture
- March 25, April 1 & 8: Measuring Knowledge: Statistics Tools for Better Discerning What Data on Student Performance Can (and Cannot) Tell Us Guada Lozano
- April 15, 22 & 29: Computational Representation Theory of Groups and Algebras Klaus Lux
- May 6: No lecture

### 2014

- Jan. 22, 29: Research Problems in Finite Element Theory: Analysis, Geometry, and Application

(Andrew Gillette) - Feb 5: No lecture
- Feb 12, 19, 26: Knot Invariants and Yang-Mills-Higgs Theory

(Sergey Cherkis) - March 5, 12, 26 & April 2nd: Scaling Limits In Random Structures

Sunder Sethuraman & Shankar Venkataramani - April 9, 16 & 23: Algorithmic Aspects of the Representation Theory of Algebras

Klaus Lux - April 30 & May 7: No lectures

### 2013

- Jan. 16, 23, 30: Geometric Flows (David Glickenstein)
- Feb. 6, 13, 20: Patterns in nature and the laboratory (Alan Newell)
- Feb 27 and Mar 6: Mathematics Education Research: What, Who and How? (Rebecca McGraw, Jennifer Eli and Mathew Felton)
- Mar 20, 27 and Apr 3: Eigenvalues and their multiplicities (Leonid Friedlander)
- Apr 10, 17, 24: (Klaus Lux)

### 2012

- Nonparametric Statistics on Manifolds - By Examples and Applications. (Rabi Bhattacharya)
- Frontier topics in algebraic geometry from scratch. (Yi Hu)
- Disorder and noise in physical systems. (Jan Wehr)
- Finite (simple) groups: classification, representations, and applications. (Pham Tiep)

### 2011

*Universality and conformal invariance in random walks*(Tom Kennedy)*Analytical Combinatorics*(Nick Ercolani and Ken McLaughlin)*The Art of Scientific Discovery*(Hermann Gordon)*Mathematical Models for the Study of Life History Strategies - Dynamics and Evolution*(Jim Cushing)*Duality in string theory*(Pan Peng)*Heron Triangles and Elliptic Curves*(William McCallum)- (Rebecca McGraw)

### 2010

*Some variational models related to liquid crystals*(Ibrahim Fatkullin)*Moduli Spaces and Geometric Invariant Theory*(Yi Hu)*Representation Theory of Finite Groups and Its Computational Aspects*(Klaus Lux)

### 2009

*Locality estimates for classical oscillator systems*(Robert Sims)*Compression and Information*(Marek Rychlik)*Geometric flows in Riemannian and discrete geometry*(David Glickenstein and Andrea Young)*Galois Groups*(Kirti Joshi and Dinesh Thakur)

### 2008

- (Moysey Brio)
- (Yi Hu)
- (Janek Wehr)
- (Klaus Lux)

### 2007

- Representation Theory of the Symmetric Group (Philip Foth)
- Quantum Graphs (Leonid Friedlander)
- Zeta function(s): A Perspective (Kirti Joshi)
- Convexity in the study of Partial Differential Relations (Shankar Venkataramani)

### 2006

- The epsilon-pseudo spectrum (Robert Indik)
- Berezian integrals (John Palmer)
- Periodically Forced Discrete Dynamical Systems and Applications to Problems in Population Dynamics (Jim Cushing)
- Counting Points on Fermat Curves (Doug Ulmer)

### 2005

- Conformal Mapping and Planar Growth Processes (Nicholas Ercolani and Shankar Venkataramani)
- Solved and Unsolved Problems in Mathematical Theory of Disordered Systems (Jan Wehr)
- Random Matrix Theory (Ken McLaughlin)
- Geometry of Polygon Spaces (Yi Hu and Philip Foth)

### 2004

- Research in Mathematics Education (Rebecca McGraw and Peter Wiles)
- The discrete Laplacian (Daniel Ueltschi)
- Some problems in the study of dynamical systems: an introduction (Don Wang)
- Gröbner bases: an introduction to algebraic geometry (Yi Hu)

### Format change

Up to academic year 2002-2003, RTG's ran on a Fall–Spring cycle. Starting with calendar year 2004, they run on a Spring–Fall cycle. Thus there were no RTGs in Fall 2003.

### 2002-2003

- Periods (Minhyong Kim)
- Random Graphs (Hermann Flaschka)

### 2001-2002

- Quantum Information (Bill Faris)
- Geometry of Polynomials (Phillip Foth and Thomas Treloar)
- Rayleigh-Ritz Calculation of the Least Eigenvalue (Marty Greenlee)

### 2000-2001

- Partition Theory (Dennis Eichhorn)
- Gaussian Theory (Maciej Wojtkowski)
- Units in p-adic domains (Romyar Sharifi)

### 1999-2000

- Cryptography (Douglas Ulmer)
- Research in Mathematics Education (Marta Civil)
- Computational Group Theory (Klaus Lux)

### 1998-1999

- Diophantine Equations (Minhyong Kim)
- Algorithms in Signal Processing (Wavelets) (Klaus Lux)
- Nonstandard Analysis (Carl DeVito)