# Andrew H N Lorent , PhD

## Assoc Professor

## Associate Professor

### French Hall

4109

A&S Mathematical Sciences - 0025

## Professional Summary

Associate Professor of Mathematics

## Education

PhD: University College London UK, 1999 (Mathematics)

Bsc: Kings College London UK, 1995 (Mathematics)

## Positions and Work Experience

10-2007 -10-2008 Emma e Giovanni Sansone Junior Visitor., Centro di Ricerca Matematica Ennio. De Giorgi., Pisa, Italy

04-2005 -10-2007 PostDoc, Max Planck Institute for Mathematics in the sciences, Leipzig, Germany

04-2003 -04-2005 EPSRC Postdoctoral fellow, Mathematical Institute, Oxford, UK

06-2002 -04-2003 PostDoc, Scuola Normale Superiore., Pisa, Italy

09-2001 -06-2002 PostDoc, Mathematics Department of the University of Jyvaskyla., Finland

10-1999 -09-2001 PostDoc, Max Planck Institute for Mathematics in the sciences, Leipzig, Germany

04-1999 -10-1999 Visitor, Mathematics Department of the University of Jyvaskyla, Finland

10-2008 -10-2014 Assistant Professor of Mathematics, University of Cincinnati,

10-2014 -To Present Associate Professor , University of Cincinnati,

## Research Support

10-21-2011 -10-23-2011 Taft Domestic Conference Travel Grant Completed Type:Grant Level:Regional

Grant: #426900 Investigators:Lorent, Andrew 09-01-2016 -08-31-2021 Simons Foundation Calculus of Variations, Quasiregular Analysis and Differential Inclusions Role:PI $7,000.00 Awarded Level:Private Non-Profit

## Abbreviated Publications

### Peer Reviewed Publications

A. Lorent, G. Peng. Regularity of the Eikonal equations with two vanishing entropies. * Ann. Inst. Poincare Anal. Non Lineaire. 35 (2018). no.2, 481-516.*

A. Lorent. Rigidity of pairs of quasiregular mappings whose symmetric part of gradient are close.* Ann. Inst. Poincare Anal. Non Lineaire. Volume 33, Issue 1, January–February 2016, Pages 23–65.*

A. Lorent. Differential inclusions, Non-absolutely convergent integrals and the first theorem of Complex Analysis. 8 pages. *Quarterly Journal of Mathematics. 65 (2014) no.4 1363-1373.*

A. Lorent. A generalized Stoilow decomposition for pairs of mappings of integrable dilatation. *Advances in Calculus of Variations. 7 (2014) no.3 327-351.*

A. Lorent. On indecomposable sets with applications. * ESIAM Control, Optimisation and Calculus of Variations. 20. (2014) no. 2, 612-631.*

A. Lorent. On functions whose symmetric part of gradient agree and a generalisation of Reshetnyak's compactness theorem.* **Calc. Var. Partial Differential Equations* 48 (2013), no. 3-4, 625–665.

J. Kinnunenm R. Korte, A. Lorent, N. Shanmugalingam. Regularity of sets with quasiminimal boundary surfaces in metric spaces.* **J. Geom. Anal. 23 (2013) no.4 1607-1640. *

A. Lorent. A simple proof of the characterization of functions of low Aviles Giga energy on a ball via regularity. * ESAIM: Control, Optimisation and Calculus of Variations. 18 (2012) 383-400.*

A. Lorent. A quantitative characterisation of functions with low Aviles Giga energy on convex domains.* Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol XII (2014) 1-66.*

R.L. Jerrard, A. Lorent. On multiwell Liouville Theorems in higher dimension. *Adv. in Calc. of Var. 6. 2013 no.3 247-298*

A. Lorent. The regularisation of the N-well problem by finite elements and by singular perturbation are scaling equivalent in two dimensions. *Control, Optimisation and Calculus of Variations*. 15 (2009), no. 2 322-366

A. Lorent . An L^p two well Liouville Theorem. *Ann. Acad. Sci. Fenn. Math*, *33 (2008).*(no. 2), 439--473.

A. Lorent. A Marstrand theorem for measures with polytope density. *Math. Ann.*, *338 (2007)*(no. 2), 451--474.

A. Lorent. The two-well problem with surface energy. *Proc. Roy. Soc. Edinburgh Sect.*, *136 (2006)*(no. 4), 795--805.

A. Lorent. A two well Liouville theorem. *Control, Optimisation and Calculus of Variations*, *11 (2005)*(no. 3), 310--356.

A. Lorent. A Marstrand type theorem for measures with cube density in general dimension. *Math. Proc. Cambridge Philos. Soc.*, *137 (2004)*(no. 3), 657--696.

A. Lorent. A generalised conical density theorem for unrectifiable sets. *Ann. Acad. Sci. Fenn. Math*, *28 (2003), no. 2*, 415--431.

A. Lorent. Rectifiability of measures with locally uniform cube density. *Proc. London Math. Soc.*, *86 (2003).*(no. 1), 153--249.

A. Lorent. An optimal scaling law for finite element approximations of a variational problem with non-trivial microstructure. *M2AN Math. Model. Numer. Anal.*, *35 (2001)*(no. 5), 921--934.

A. Lorent, G. Peng. On the Rank-1 convex hull of a set arising from a hyperbolic system of Lagrangian elasticity. *Calc. Var. Partial Differential Equations 59 (2020), no. 5, Paper No. 156, 36 pp.*

A. Lorent, G. Peng. Null Lagrangian Measures in Subspaces, Compensated Compactness and Conservation Laws. *Arch Rational Mech Anal. November (2019), Volume 234, Issue 2, pp 857–910*

X. Lamy, A. Lorent, G. Peng. Rigidity of a non-elliptic differential inclusion related to the Aviles-Giga conjecture.

* Arch. Ration. Mech. Anal. 238 (2020) no.1 383-413 *

### In Press

A. Lorent. G. Peng. Factorization for entropy production of the Eikonal equation and regularity. *To appear in Indiana University Mathematics Journal*

## Presentations

### Invited Presentations

Andrew Lorent
(01-29-2011. )
*Functions whose symmetric part of gradient agree and generalizations of Reshetnyak's compactness theorem *.Ohio River Analysis meeting, University of Cincinnati.
Level:National

Andrew Lorent
(03-12-2011. )
*Functions whose symmetric part of gradient agree and a generalization of Reshetnyak's compactness Theorem *.AMS Special Session on Geometric Mapping Theory in Euclidean and Non-Euclidean Spaces , Georgia Southern University, Statesboro..
Level:National

Andrew Lorent
(02-11-2011. )
*Characterizing the Minimizers of the Aviles Giga Functional, A Survey and Some Recent Results *.PDE seminar , Maths Department University of Purdue.
Level:Regional

Andrew Lorent
(Bad Format: 20111404. )
*Functions whose symmetric part of gradient agree and generalizations of Reshetnyak's compactness theorem. *PDE seminar., Mathematics Department. University of Pittsburgh.
Level:Regional

Andrew Lorent
(09-10-2011. )
*Multiwell Liouville theorems and pairs of functions whose symmetric part of gradient are close *.AMS Special Session on Geometric Aspects of Analysis and Measure Theory , Cornell. Ithaca, NY.
Level:National

Andrew Lorent
(10-22-2011. )
*On the problem of characterizing the minimizers of the Aviles Giga functional. *AMS Special Session on Applied Analysis, University of Utah, Salt Lake City, UT .
Level:National

Andrew Lorent
(09-2010. )
*Rigidity of functions whose gradient is close to SO(n) and Liouville Theorems. *.‘Inequalities and PDEs’ conference Male Ciche, Zakopane. Poland. .
Level:International

Andrew Lorent
(03-2010. )
*A characterisation of minimisers of the Aviles Giga functional with low energy *.AMS special session on Partial Differential Equations in Geometry and Variational Problems , Kentucky.
Level:Regional

Andrew Lorent
(12-2009. )
*Low energy solutions of the Aviles Giga energy *.Mathematics Department University of Warsaw .
Level:National

Andrew Lorent
(06-2009. )
*Quantitative Liouville Theorems *.Math Department. University of Jyväskylä ,
Level:International

Andrew Lorent
(02-2009. )
*Quantitative Liouville Theorems *.Math Department , University of Kentucky .
Level:Regional

Andrew Lorent
(10-19-2013. )
*A generalized Stoilow decomposition for pairs of mappings of integrable dilatation. *AMS Fall Central Sectional Meeting, Washington University, St. Louis, MO .
Level:National

Andrew Lorent
(07-2015. )
*The Aviles Giga functional past and present *.Conference "Geometric Measure Theory and Calculus of Variations", Institute Fourier. Grenoble, France. .
Level:International

Andrew Lorent
(04-2015. )
*Rigidity of pairs of quasiregular mappings whose symmetric part of gradient are close. *PDE seminar, University of Purdue.
Level:National

Andrew Lorent
(10-2015. )
*Marstard's Theorem and other rectifiablity and density results in non Euclidean spaces *.Rainwater seminar, Washington University, Seattle .
Level:National

Andrew Lorent
(01-2016. )
* The Aviles Giga functional. A history,a survey and some new results *.PDE Seminar, University of Indiana in Bloomington..
Level:National

Andrew Lorent
(09-2016. )
*An absolute three well Liouville theorem *. Special session on Nonlinear Partial Differential Equations in Material Science and Mathematical Biology. AMS 2016 , Fall Eastern Sectional Meeting. Bowdoin College, Brunswick, ME. .
Level:National

Andrew Lorent
(01-2017. )
* The Eikonal Equation with two vanishing entropies *.Analysis Seminar, University of Illinois., Urbana-Champaign..
Level:National

Andrew Lorent
(02-2017. )
*The Eikonal Equation with two vanishing entropies *. Analysis Seminar, University of Warwick., Warwick UK.
Level:International

Andrew Lorent
(03-2017. )
* The Eikonal Equation with two vanishing entropies *. Analysis Seminar. University of Zurich, Zurich. Switerland.
Level:International

Andrew Lorent
(04-2018. )
*The Aviles-Giga functional - A history, a survey and some new results. *.PDE seminar. University of Minnesota., Minnesota. .
Level:National

Andrew Lorent
(04-2018. )
* Null Lagrangian Measures in planes, compensated compactness and conservation laws. * Special Session on Analysis and Geometry in Nonsmooth Spaces, II. AMS Spring Eastern Sectional Meeting Northeastern University, Boston, MA, Boston.
Level:National

Andrew Lorent
(02-2019. )
* Null Lagrangian Measures in planes, compensated compactness and conservation laws. *GMT workshop. Johns Hopkins, Baltimore.
Level:National

Andrew Lorent
(03-20-2019. )
*Null Lagrangian Measures *.83rd Midwest PDE Meeting, Indiana University.
Level:National

Andrew Lorent
(03-23-2019. )
*Null Lagrangian Measures *.Workshop ”Variational Problems in Physics”, Toulouse, France.
Level:International

Andrew Lorent
(12-12-2019. )
*Null Lagrangian Measures *.Special session. SIAM Conference on PDE, LA Quinta, California. .
Level:National

## Honors and Awards

2000 -2002 EPDI PostDoctoral fellow

## Service

(GSEC ) Committee Member Type:Departmental Service Level:Department 02-02-2011 -02-02-2012

(Linear Algebra ) Committee Member Type:Departmental Service Level:Department 01-04-2011 -01-06-2011

MathSciNet Reviewer Type:Editorial Service Level:International

Crelle's Journal Peer Review/Referee Type:Editorial Service Level:International

(Undergraduate math major advisor ) Type:Departmental Service Level:Department

Graduate student advisor Type:Departmental Service Level:Department

Organizer of the Geometric Analysis seminar Type:Departmental Service Level:Department 08-2008 -08-2016

Transactions American Mathematical Society Peer Review/Referee Type:Editorial Service Level:International

Siam Journal of Mathematical Analysis Peer Review/Referee Type:Editorial Service Level:International

Nonlinearity Peer Review/Referee Type:Editorial Service Level:International

Proceeding Cambridge Philosophical Society Peer Review/Referee Type:Editorial Service

Demonstratio Mathematica Peer Review/Referee Type:Editorial Service Level:International

(Executive ) Committee Member Type:Departmental Service 08-01-2013 -08-01-2014

(Hiring ) Committee Member Type:Departmental Service 08-01-2013 -To Present

Proceedings London Mathematical Society Peer Review/Referee Type:Editorial Service Level:International

(Taft executive commitee ) Committee Member Type:University/College Service Level:University 2014 -To Present

Graduate student adviser Type:Departmental Service Level:Department 2017 -To Present

## Professional Affiliation

1998 -To Present: London Mathematical Society,

2011 -To Present: American Mathematics Society,

## Courses Taught

15-MATH-553 PDE & FOURIER ANAL Level:Undergraduate

15-MATH-264 CALC & AN GEOM IV Level:Undergraduate

15-MATH-506 ADVANCED CALCULUS Level:Undergraduate

15-MATH-554 PDE & FOURIER ANAL Level:Undergraduate

15-MATH-603 COMPLEX ANALYSIS I Level:Graduate

15-MATH-264 CALC & AN GEOM IV Level:Undergraduate

15-MATH-252 CALCULUS II Level:Undergraduate

15-MATH-352 LINEAR ALGEBRA II Level:Undergraduate

15-MATH-253 CALCULUS III Level:Undergraduate

15-MATH-253 CALCULUS III Level:Undergraduate

15-MATH-629 PART DIFFER EQUATNS Level:Graduate

15-MATH-352 LINEAR ALGEBRA II Level:Undergraduate

15-MATH-351 LINEAR ALGEBRA I Level:Undergraduate

15-MATH-629 PART DIFFER EQUATNS Level:Graduate

15-MATH-251 CALCULUS I Level:Undergraduate

15-MATH-351 LINEAR ALGEBRA I Level:Undergraduate

15-MATH-627 PART DIFFER EQUATNS Level:Graduate

15-MATH-601 COMPLEX ANALYSIS I Level:Graduate

15-MATH-602 COMPLEX ANALYSIS I Level:Graduate

15-MATH-1061 CALCULUS I Level:Undergraduate

15-MATH-2063 MULTIVARIABLE CALCULUS Level:Undergraduate

15-MATH-351 LINEAR ALGEBRA I Level:Undergraduate

15-MATH-161Z CALCULUS I

## Faculty Development Activities

09-27-2012 -11-08-2012 Formative Peer Review of Teaching CET&L Type:Workshop