Andrew H N Lorent , PhD

 Associate Professor of Mathematics 

 

PhD: University College London UK, 1999 (Mathematics)

Bsc: Kings College London UK, 1995 (Mathematics)

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,

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

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

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

2000 -2002 EPDI PostDoctoral fellow

(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

1998 -To Present: London Mathematical Society,

2011 -To Present: American Mathematics Society,

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

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