# Tayyab Nawaz

Email: tnawaz2@illinois.edu

**Office:** Room 108 Altgeld Hall

I am a graduate student in the Department of Mathematics at the University of Illinois at Urbana-Champaign(UIUC), studying mean-field models and spin glass systems from statistical mechanics using different tools from probability
theory under supervision of Kay Kirkpatrick. I did my MS in Applied Mathematics from Department of Mathematics at UIUC in 2013 under supervision of
Richard Sowers, where in my Master's thesis I have studied the dynamics of New York stock market.

**Research Interests:**

Probability theory and Statistical Mechanics. In particular, my current research focuses on mean-field classical N-vector models, which are important in mathematical
physics. I am studying the spin glass systems using theory of large deviations and Stein's method to come up with probablistics results such as law of large number, central limit theorem and probability density function.
Scaling limits of the physical systems: I am interested in studying the phase transitions of the O(N) models and the behaviour of physical quantities such as magnetization, temperature, specific heat, susceptibility near continuous
phase transitions.
Financial Data Analysis: One of my interest is to develop computational algorithm to study the patterns in some given data. Prevsiouly i have written some python based algorithm to read the data from New York stock market to
analyize it for implied volatility and hard to borrow stocks. Currently, I am working on CIR model to calculate the conditional moments for the conditinal Asian options.
Multigrid Monte-Carlo Methods: I am interested in finding the optimal algorithm to study the energy minimization problem related to these O(N) models. Some open computational statistics questions are: critical dimension,
computational complexity of the multigrid Monte-Carlo algorithms, universality of the criticl exponets for these O(N) models.
My Research statement is available here.
**Education:**

PhD Mathematics with Computational Science and Engineering, Mathematics Department, UIUC USA, 2013-Present.
MS in Applied Mathematics, Mathematics Department, UIUC USA, 2010-2013.
BS Mathematics, Mathematics Department, COMSATS Institute of Information Technology (CIIT), Islamabad Pakistan, 2004-2008.

** Academic Positions:**

Research Assistant (REGS) , UIUC Spring 2017.
Teaching Assistant, UIUC USA 2012-2016.
Research Assistant, UIUC USA Fall 2015, Summer 2016.
Program Associate, MSRI Berkeley USA Aug 2015-Sep 2015.
Research Assistant, CIIT Islamabad, Pakistan 2009-2010.

** Publications:**

Kirkpatrick, K. and Nawaz, T. Asymptotics of mean-field O(N) models. J. Stat. Phys. (2016) Vol. 165, Issue 6:1114--1140.
Kirkpatrick, K. and Nawaz, T. Critical behavior of mean-field XY and related models. To appear in Birkhauser Proceedings of the Conference in honor of Rodrigo Bañuelos.
Master's Thesis
Graphical analysis of Hard to borrow stocks

** In prepration:**
Nawaz,T. Critical exponents of mean-field O(N) models.
PhD Thesis: Applications of Stein's method and Large Deviaton Principle's in mean field O(N) models

** Teaching:**

I have been a part of the online NetMath program of the Department of Mathematics, UIUC since 2012 and have mentored the following courses:
Math 286 Differential Equations Plus ,Summer 2016, Fall 2016.
Math 124 Finite Mathematics ,Spring 2016.
Math 285 Differential Equations , Summer 2015.
Math 292 Vector Calculus ,Spring 2015.
Math 220 Calculus I , Fall 2014.
Math 461 Introduction to Probability Theory , Summer 2014, Spring 2014.
Math 231 Calculus III , Fall 2013.
Math 241 Calculus II , Summer 2013.
Math 415 Applied Linear Algebra , Fall 2012 , Spring 2013.
** Courseware Development:**

I have updated/revised the Mathematica based courseware for the following courses
Math 124 Finite Mathematics
Math 461 Introduction to Probability Theory

** Honors and Awards:**

AMS travel grants (Spring 2016, Fall 2016)
UIUC-USA Net-Math TA Service Award (Fall 2013)
UIUC-USA Fellowship for MS Mathematics (2010-2012)
CIIT, Islamabad Pakistan Chancellors Gold Medal (2008)
CIIT, Islamabad Pakistan Campus Gold Medal (2008)
CIIT, Islamabad Pakistan Tuition waiver throughout BS Mathematics.(2004-2008)
CIIT, Islamabad Pakistan Cash award in all semester's during BS Mathematics. (2004-2008)

** Mentoring Experience:**

During Fall 2014, as a member of Illinois Geometory Lab (Dept. of Mathematics, UIUC) I have mentored three undergraduate students for spin-glass project
from statistical physics. I helped them with model setup, parameter's significance and python based environment for simulations. Here is the poster for the IGL project.
** Referee for Journals:**

Proceedings of the National Academy of Sciences (PNAS)

** Talks:**

Graduate Colloquium, Department of Mathematics, February 2017 UIUC USA
Special Session on New Developments in the Analysis of Nonlocal Operators , October 2016 University of St. Thomas USA.
Great Lakes Mathematical Physics Meeting, June 2016 Michigan State University USA.
Special Session on Discrete Probability, April 2016 North Dakota State University USA.
Prairie Analysis Seminar September 2015, Kansas State University USA.
Mathematical Sciences Research Institute, Graduate Seminar September 2015 Berkeley USA.