# Tom Alberts

#### University of Utah

#### Department of Mathematics

I am currently an assistant professor in the Department of Mathematics at the University of Utah. My research is focused on probability theory.

Prior to being at Utah, I was the Scott Russell Johnson Senior Postdoctoral Fellow in the Department of Mathematics at Caltech, and an NSERC Postdoctoral Fellow in the Department of Mathematics at the University of Toronto. I completed my graduate studies at the Courant Institute of Mathematical Sciences at New York University. My thesis advisor was Scott Sheffield.

### Contact Information

lastname (at) math (dot) utah (dot) edu

#### Office Location

LCB 114

Phone: 801-585-1643

#### Mailing Address

Tom Alberts

Department of Mathematics, University of Utah

155 S 1400 E Room 233

Salt Lake City, UT 84112-0090

### Research

My main focus of research is in probability theory, and within that I mostly study two-dimensional conformally invariant systems. The basic model of these are the Schramm-Loewner Evolution and its variants. I also have interests in statistical mechanics, random walks in random environments, directed polymer models, last passage percolation, and random matrix theory.

### Publications

Nested Critical Points for a Directed Polymer on a Disordered Diamond Lattice.

Alberts T. & Clark J.,*arXiv:1602.06629 [math.PR]*. (2016).Bak-Sneppen Backwards.

Alberts T. & Lee G.-Y. & Simper M.,*arXiv:1510.04114 [math.PR]*. (2015).The Intermediate Disorder Regime for a Directed Polymer Model on a Hierarchical Lattice.

Alberts T. & Clark J. & Kocic S.,*arXiv:1508.04791 [math.PR]*. (2015).A Dimension Spectrum for SLE Boundary Collisions.

Alberts T. & Binder I. & Johansson Viklund F.,*Communications in Mathematical Physics*,**343**, no. 1, 273-298. (2016). Online Journal.Diffusions of Multiplicative Cascades.

Alberts T. & Rifkind B.,*Stochastic Processes and their Applications*,**124**, no. 2, 1141-1169. (2014). Online Journal.Intermediate Disorder for 1+1 Dimensional Directed Polymers.

Alberts T. & Khanin K. & Quastel J.,*Annals of Probability*,**42**, no. 3, 1212-1256. (2014). Online Journal.The Continuum Directed Random Polymer.

Alberts T. & Khanin K. & Quastel J.,*J. Stat. Phys.*,**154**, no. 1-2, 305-326. (2014). Online Journal.Some Partial Results on the Convergence of Loop-Erased Random Walk to SLE(2) in the Natural Time Parameterization.

Alberts T. & Kozdron M. & Masson R.,*J. Stat. Phys.*,**153**, no. 1, 119-141. (2013). Online Journal.The Near-Critical Scaling Window for Directed Polymers on Disordered Trees.

Alberts T. & Ortgiese M.,*Electronic Journal of Probability*,**18**, no. 19, 24 pp. (2013). Online Journal.The Green's function for the radial Schramm-Loewner Evolution.

Alberts T. & Kozdron M. & Lawler G.,*J. Phys. A*,**45**, 494015, 17 pp. (2012). Online Journal.The Covariant Measure of SLE on the Boundary.

Alberts T. & Sheffield S.,*Probability Theory and Related Fields*,**3-4**, 331-371. (2011). Online Journal.The Intermediate Disorder Regime for Directed Polymers in Dimension 1+1.

Alberts T. & Khanin K. & Quastel J.,*Physical Review Letters*,**105**, 090603. (2010). Online Journal.Bridge Decomposition of Restriction Measures.

Alberts T. & Duminil-Copin H.,*Journal of Statistical Physics*,**140, 3**, 467-493. (2010). Online Journal.Hausdorff Dimension of the SLE Curve Intersected with the Real Line.

Alberts T. & Sheffield S.,*Electronic Journal of Probability*,**40**, 1166-1188. (2008). Online JournalIntersection Probabilities for a Chordal SLE Path and a Semicircle..

Alberts T. & Kozdron M.,*Electronic Communications in Probability*.**13**, 448-460. (2008). Online JournalA Locally Adaptive Transformation Method of Boundary Correction in Kernel Density Estimation.

Karunamuni R.J. & Alberts T.,*Journal of Statistical Planning and Inference***136**, 2936-2960. (2006). Online JournalA Generalized Reflection Method of Boundary Correction in Kernel Density Estimation.

Karunamuni R.J. & Alberts T.,*Canadian Journal of Statistics*,**33**, 497-509. (2005). Online Journal.On Boundary Correction in Kernel Density Estimation.

Karunamuni R.J. & Alberts T.,*Statistical Methodology*,**2**, 191-212. (2005). Online Journal__A Semiparametric Method of Boundary Correction for Kernel Density Estimation__.

Alberts T. & Karunamuni R.J.,*Statistics and Probability Letters*,**61**, 287-298. (2003). Online Journal

### Slide Presentations

### Teaching

#### University of Utah

#### Caltech

- Introduction to Unitary Group Representations, Winter 2014
- Probability I, Fall 2013
- Statistics, Winter 2013
- Stochastic Analysis, Fall 2012
- Probability II, Winter 2012
- Probability I, Fall 2011

#### University of Toronto

- Introduction to Stochastic Processes, Spring 2011
- Partial Differential Equations, Fall 2010
- Introduction to Mathematical Finance, Fall 2009
- Introduction to Stochastic Processes, Spring 2009

#### New York University

- Financial Econometrics and Statistical Arbitrage, Fall 2007
- Interest Rate and Credit Models, Summer 2007
- Interest Rate and Credit Models, Spring 2007
- Financial Econometrics and Statistical Arbitrage, Fall 2006
- Calculus II, Summer 2006
- Risk Management, Spring 2006
- Computing in Finance, Fall 2005
- Calculus I, Summer 2005
- Stochastic Calculus, Spring 2005
- Computing in Finance, Fall 2004
- Business Calculus, Summer 2004
- Business Calculus, Spring 2004