## About me

I am an associate professor of Mathematics at Loyola Marymount University. My research interests are in Deep Learning, Machine Learning and Partial Differential equations.

I did my PhD at Duke University with Prof. Michael Reed, and my postdoc at UCLA with Prof. Andrea Bertozzi. Before joining LMU I was an assistant professor at UCR.

## Machine Learning and Deep Learning Publications

C. K. Joshi, T. Laurent and X. Bresson

**On Learning Paradigms for the Travelling Salesman Problem**

NeurIPS 2019 workshop on Graph Representation Learning [paper]

X. Bresson and T. Laurent

**A Two-Step Graph Convolutional Decoder for Molecule Generation**

NeurIPS 2019 workshop on Machine Learning and the Physical Sciences [paper]

T. Laurent and J. von Brecht

**The Multilinear Structure of ReLU Networks**

ICML 2018 [paper] [video]

T. Laurent and J. von Brecht

**Deep linear neural networks with arbitrary loss: All local minima are global**

ICML 2018 [paper] [video]

X. Bresson and T. Laurent

**An Experimental Study of Neural Networks for Variable Graphs**

ICLR 2018 (workshop track) [paper]

X. Bresson, H. Hu, T. Laurent, A. Szlam and J. von Brecht

**An incremental reseeding strategy for clustering**

Mathematics and Visualization, 2018 [paper]

T. Laurent and J. von Brecht

**A recurrent neural network without chaos**

ICLR 2017 [paper]

X. Bresson, T. Laurent, A. Szlam and J. von Brecht

**The product cut**

NIPS 2016 [paper]

N. Garcia, D. Slepcev, J. von Brecht, T. Laurent, and X. Bresson

**Consistency of Cheeger and ratio graph cuts**

JMLR, volume 17, 2016 [paper]

X. Bresson, T. Laurent and J. von Brecht

**Enhanced lasso recovery on graph**

European Signal Processing Conference (EUSIPCO), 2015 [paper]

X. Bresson, T. Laurent, D. Uminsky and J. von Brecht

**Multiclass total variation clustering**

NIPS 2013 [paper]

H. Hu, T. Laurent, M. A. Porter and A. L. Bertozzi

**A method based on total variation for network modularity optimization using the MBO scheme**

SIAM J. Appl. Math., 73(6), pp. 2224-2246, 2013 [paper]

X. Bresson, T. Laurent, D. Uminsky and J. von Brecht

**Convergence and energy landscape for Cheeger cut clustering**

NIPS 2012 [paper]

## Partial Differential Equations Publications

A. Bertozzi, J. Garnett, T. Laurent and J. Verdera

**The regularity of the boundary of a multidimensional aggregation patch**

SIAM J. Math. Anal., 48(6), 3789-3819, 2016 [paper]

S. Ramakrishnan, T. Laurent, M. Kumar, and A. Bertozzi

**A spatiotemporal chemotactic model for ant foraging**

Modern Physics Letters B, Vol. 28, No. 30, 2014

D. Balague, J. A. Carrillo, T. Laurent and G. Raoul

**Dimensionality of Local Minimizers of the Interaction Energy**

Archive for Rational Mechanics and Analysis, Volume 209, Issue 3, pp 1055-1088, 2013 [paper]

D. Balague, J. A. Carrillo, T. Laurent and G. Raoul

**Nonlocal interactions by repulsive-attractive potentials: radial in/stability**

Physica D: Nonlinear Phenomena, 2012 [paper]

A. Bertozzi, T. Laurent and F. LeĢger

**Aggregation and spreading via the Newtonian potential: the dynamics of patch solutions**

Mathematical Models and Methods in Applied Sciences, 22, (2012)

A. Bertozzi, J. Garnett and T. Laurent

**Characterization of radially symmetric finite time blowup in multidimensional aggregation equations**

SIAM J. Math. Anal., 44, No 2 (2012), pp. 651-681

J. A. Carrillo, M. DiFrancesco, A. Figalli, T. Laurent and D. Slepcev

**Confinement in nonlocal interaction equations**

Nonlinear Analysis, 75 (2012), pp. 550-558

J. A. Carrillo, M. DiFrancesco, A. Figalli, T. Laurent and D. Slepcev

**Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations**

Duke Math. J., 156, No 2 (2011), pp. 229-271 [paper]

A. Bertozzi, T. Laurent and J. Rosado

**Lp Theory for the Multidimensional Aggregation Equation**

Communications on Pure and Applied Mathematics, 64, No 1 (2011), pp. 45-83

A. Bertozzi and T. Laurent

**The Behavior of Solutions of Multidimensional Aggregation Equations with Mildly Singular interaction Kernels**

Chinese Annals of Mathematics, Special Majda issue, 30, No 5 (2009), pp. 463-482

A. Bertozzi, J. A. Carrillo and T. Laurent

**Blowup in multidimensional aggregation equations with mildly singular interaction kernels**

Nonlinearity, 22, No 3 (2009), pp. 683-710

A. Bertozzi and T. Laurent

**Finite-time Blow-up of Solutions of an Aggregation Equation in Rn**

Comm. Math. Phys., 274, No 3 (2007), pp. 717-735

T. Laurent

**Local and Global Existence for an Aggregation Equation**

Communications in Partial Differential Equations, 32, No 12 (2007), pp. 1941-1964

T. Laurent, B. Rider and M. Reed

**Parabolic Behavior of a Hyperbolic Delay Equation**

SIAM J. Math. Anal. 38, No 1 (2006), pp. 1-15