Gareth James Speight, MMath PhD

I enjoy mathematical analysis that has a geometric flavour. I am particularly interested in geometric measure theory, real analysis, analysis on metric spaces, metric geometry and subriemannian geometry. You can find more information on my webpage.

From January 2016 I am co-organizer of the UC Analysis and PDE seminar.

Between September 2013 and May 2015 I was a postdoctoral researcher in the ERC project Geometric Measure Theory in non-Euclidean Spaces at the Scuola Normale Superiore di Pisa in Italy. My advisor was Luigi Ambrosio.

I obtained my PhD in June 2013 from the Mathematics Institute at the University of Warwick in the United Kingdom. My supervisor was David Preiss.

PhD: University of Warwick UK, 2013 (Mathematics)

MMath: University of Warwick UK, 2009 (Mathematics)

Geometric measure theory, analysis on metric spaces, subriemannian geometry, metric geometry, real analysis.

09-2013 -05-2015 Postdoctoral Researcher, Scuola Normale Superiore di Pisa, Pisa, Italy

01-2016 Faculty Development Fund, University of Cincinnati Domestic Conference Travel Grant to give an invited talk at the Joint Mathematics Meetings 2016 in Seattle $1257

03-2016 Taft Research Center Domestic Conference Travel Grant to give an invited talk at the AMS 2016 Spring Eastern Sectional Meeting $810

05-2016 -08-2016 Taft Research Center Taft Summer Research Fellowship $8000

04-2016 -05-2016 Taft Research Center Taft Research Support Grant for Collaboration on Differentiability of Lipschitz Functions in Carnot Groups $1413

06-2017 Faculty Development Fund Travel grant for summer research travel in 2017. $1970

07-2017 -06-2019 American Mathematical Society and Simons Foundation AMS Simons Travel Grant $4000 Type:Grant

Grant: #DMS-1700077 Investigators:Michael Goldberg, Leonid Slavin, Gareth Speight 02-01-2017 -01-31-2020 National Science Foundation Collaborative Research: Ohio River Analysis Meetings 2017-2019 Role:Co-PI $28,000

05-2018 -08-2018 Taft Research Center International Conference Travel Grant $2700

05-2018 Taft Research Center Research Support Grant for research on Geometry and Differentiability in Carnot Groups $2094

05-2019 -06-2019 University of Trento Visiting Professor at the University of Trento $4200

Grant: #576219 Investigators:Gareth Speight 09-2018 -08-2023 Simons Foundation Simons Collaboration Grant: Geometry of Lipschitz Maps and Carnot Groups Role:PI $42,000

05-2019 -08-2019 Taft Research Center Taft Summer Research Fellowship $8000

Grant: #NSF 1856471 Investigators:Speight, Gareth 09-01-2019 -08-31-2020 National Science Foundation Latest in Geometric Analysis Role:PI $44,603 Type:Grant

Grant: #NSF DMS-2000250 Investigators:Michael Goldberg, Leonid Slavin, Gareth Speight 02-2020 -01-2022 National Science Foundation Collaborative Research: Ohio River Analysis Meetings 2020–2022 Role:Co-PI $16,000 Type:Grant

Grant: #576219 Investigators:Speight, Gareth 09-01-2018 -08-31-2023 Simons Foundation Geometry of Lipschitz Maps and Carnot Groups (Speight) Role:PI $8,400.00 Active Level:Private Non-Profit

Grant: #DMS-2000161 Investigators:Goldberg, Michael; Slavin, Leonid; Speight, Gareth 02-01-2020 -01-31-2023 National Science Foundation Collaborative Research: Ohio River Analysis Meetings 2020-2022 Role:Collaborator $16,000.00 Awarded Level:Federal

Grant: #DMS-2348715 Investigators:Speight, Gareth 09-01-2024 -08-31-2027 National Science Foundation Differentiability in Carnot Groups and Metric Measure Spaces Role:PI 263078.00 Active Level:Federal

Grant: #DMS-244520-000 Investigators:Goldberg, Michael; Slavin, Leonid; Speight, Gareth 03-01-2025 -02-29-2028 National Science Foundation Collaborative Research: Conference: Ohio River Analysis Meetings 2025-2027 Role:PI 32000.00 Awarded Level:Federal

Peer Reviewed Publications

D. Bate and G. Speight  (2013). Differentiability, Porosity and Doubling in Metric Measure Spaces. Proceedings of the American Mathematical Society, 141, 971-985

journal paper

G. Speight  (2016). Lusin Approximation and Horizontal Curves in Carnot Groups. Revista Matematica Iberoamericana, 32 (4) , 1425-1446

journal paper

G. Speight  (2013). Surfaces Meeting Porous Sets in Positive Measure. Israel Journal of Mathematics, 196 (1) , 435-460

journal paper

G. Speight  (2013). Directional Lower Porosity. Real Analysis Exchange , 39 (1) , 45-56

journal paper

D. Preiss and G. Speight  (2015). Differentiability of Lipschitz Functions in Lebesgue Null Sets. Inventiones Mathematicae, 199 (2) , 517-559

journal paper

S. Di Marino and G. Speight  (2015). The p-Weak Gradient Depends on p. Proceedings of the American Mathematical Society, 143, 5239-5252

journal paper

L. Ambrosio and A. Pinamonti and G. Speight  (2019). Weighted Sobolev Spaces on Metric Measure Spaces. Journal fur die reine und angewandte Mathematik (Crelle's Journal), 746, 39-65

journal paper

L. Ambrosio and A. Pinamonti and G. Speight  (2015). Tensorization of Cheeger Energies, the Space H^{1,1} and the Area Formula for Graphs. Advances in Mathematics, 281, 1145-1177

journal paper

A. Pinamonti and G. Speight  (2017). A Measure Zero Universal Differentiability Set in the Heisenberg Group. Mathematische Annalen, 368 (1) , 233--278

journal paper

E. Le Donne and G. Speight  (2016). Lusin Approximation for Horizontal Curves in Step 2 Carnot Groups. Calculus of Variations and Partial Differential Equations, 55 (5) , 1--22

journal paper

A. Pinamonti and G. Speight  (2017). Porosity, Differentiability and Pansu's Theorem. Journal of Geometric Analysis, 27 (3) , 2055–2080

journal paper

A. Pinamonti and G. Speight  (2017). Structure of Porous Sets in Carnot Groups. Illinois Journal of Mathematics, 61 (1-2) , 127-150

journal paper

A. Pinamonti and G. Speight  (2017). Expository Article describing A Measure Zero Universal Differentiability Set in the Heisenberg Group. Bruno Pini Mathematical Analysis Seminar, Feb. 2017, 85-96

seminar paper

E. Le Donne, A. Pinamonti and G. Speight  (2019). Universal Differentiability Sets and Maximal Directional Derivatives in Carnot Groups. Journal de Mathematiques Pures et Appliquees, 121, 83-112

journal paper

V. Magnani, A. Pinamonti and G. Speight  (2020). Porosity and Differentiability of Lipschitz Maps from Stratified Groups to Banach Homogeneous Groups. Annali di Matematica Pura ed Applicata, 199, 1197-1220

journal paper

P. Lahti, L. Maly, N. Shanmugalingam and G. Speight  (2019). Domains in Metric Measure Spaces with Boundary of Positive Mean Curvature, and the Dirichlet Problem for Functions of Least Gradient. Journal of Geometric Analysis, 29 (4) , 3176–3220

journal paper

A. Pinamonti and G. Speight  (2020). Universal Differentiability Sets in Carnot Groups of Arbitrarily High Step. Israel Journal of Mathematics, 240, 445-502

preprint

A. Pinamonti, G. Speight, S. Zimmerman  (2019). A C^m Whitney Extension Theorem for Horizontal Curves in the Heisenberg Group. Transactions of the American Mathematical Society, 371 (12) , 8971-8992

journal paper

M. Capolli, A. Pinamonti and G. SpeightA C^m Lusin Approximation Theorem for Horizontal Curves in the Heisenberg Group. Calculus of Variations and Partial Differential Equations

preprint

A. Maaloui, A. Pinamonti, G. SpeightFunction Spaces via Fractional Poisson Kernel on Carnot Groups and Applications. preprint submitted for publication

S. Eriksson-Bique, G. Giovannardi, R. Korte, N. Shanmugalingam, G. SpeightRegularity of Solutions to the Fractional Cheeger-Laplacian on Domains in Metric Spaces of Bounded Geometry. preprint submitted for publication

Invited Presentations

(03-2015. ) Differentiability of Lipschitz Functions and Curves in Carnot Groups .Geometry Seminar, University of Jyvaskyla, Finland.

(01-2015. ) Differentiability of Lipschitz Functions and Curves in Carnot Groups .Colloquium, University of Cincinnati, US.

(01-2015. ) Differentiability of Lipschitz Functions and Curves in Carnot Groups .University of Bath, UK.

(12-2013. ) Porosity and Differentiability .Leipzig, Germany.

(11-2013. ) Porosity and Differentiability .Analysis Seminar, Innsbruck, Austria.

(10-2013. ) Porosity and Differentiability .ERC Workshop on Geometric Measure Theory, Analysis in Metric Spaces and Real Analysis, Pisa, Italy.

(01-2013. ) Porosity and Differentiability .Albert Einstein Institute, Potsdam, Germany.

(01-2016. ) A Measure Zero Universal Differentiability Set in the Heisenberg Group .AMS Special Session on Analysis and Geometry in Nonsmooth Metric Measure Spaces, JMM 2016, Seattle, USA.

(03-2016. ) A Measure Zero Universal Differentiability Set in the Heisenberg Group .AMS Special Session on Geometric Measure Theory and Its Applications, AMS Spring 2016 Eastern Sectional Meeting, SUNY Stony Brook, USA.

(06-2016. ) Differentiability in Carnot Groups .University of Warwick, UK.

(06-2016. ) Lusin Approximation and Differentiability in Carnot Groups .Conference on Singular Phenomena and Singular Geometries, University of Pisa, Italy.

(10-2016. ) Differentiability of Lipschitz maps in Euclidean spaces and Carnot groups .Analysis Seminar, University of Illinois at Urbana-Champaign.

(03-2017. ) Porosity and Differentiability in Euclidean Spaces and Carnot Groups .Conference on Analysis on Metric Spaces, University of Pittsburgh.

(06-2017. ) Maximal directional derivatives and universal differentiability sets in Carnot groups .23rd Rolf Nevanlinna Conference, ETH Zurich, Switzerland.

(06-2017. ) Maximal directional derivatives and universal differentiability sets in Carnot groups .University of Trento, Italy.

(07-2017. ) Maximal directional derivatives and universal differentiability sets in Carnot groups .Geometric Measure Theory Conference, University of Warwick, UK.

(03-2018. ) Differentiability of Lipschitz Maps in Euclidean Spaces and Carnot Groups .Colloquium, Ball State University.

(09-2018. ) Fall Eastern Sectional Meeting, University of Delaware.

(10-2018. ) SIAM Central States Sectional Meeting, University of Oklahoma.

(02-2019. ) Workshop in Geometric Measure Theory, Johns Hopkins University.

(03-2019. ) AMS Spring Central and Western Joint Sectional Meeting, University of Honolulu.

(04-2019. ) AMS Spring Eastern Sectional Meeting, University of Connecticut.

(05-2019. ) Colloquium, Bowling Green State University.

(05-2019. ) Three Analysis Seminars, University of Trento, Italy.

(09-2019. ) AMS Fall Central Sectional Meeting, University of Wisconsin-Madison.

(11-2019. ) Latest in Geometric Analysis, Bedlewo, Poland.

2013 Warwick Faculty of Science Doctoral Thesis Award University of Warwick Status:Recipient

2013 Warwick Award for Teaching Excellence for Postgraduate Research Students Status:Nomination

Marco Capolli (PhD co-supervisor with Andrea Pinamonti) (Doctoral ) Status:In Progress

MathSciNet Mathematical Reviews Reviewer Type:Service to Professional Associations 2013 -To Present

International Mathematics Research Notices Peer Review/Referee

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze Peer Review/Referee

Bulletin of the London Mathematical Society Peer Review/Referee

(Master of Science Oral Exam Committee for Chris Foster (12/2015), Mehmet Ozdemir (12/2015), Brian Reid (04/2019) ) Member Type:Departmental Service Level:Department

Organizer of the UC Analysis and PDE Seminar Type:Departmental Service 2016 -To Present

(Visiting Assistant Professor Hiring Committee ) Member Type:Departmental Service 2016

(Graduate Student Evaluation Committee ) Member Type:Departmental Service 2016 -To Present

(Organizing Committee for the Ohio River Analysis Meeting (ORAM) ) Member Type:Departmental Service 2016 -To Present

(Executive Committee ) Member Type:Departmental Service 2016

(Graduate Advisor Committee ) Member Type:Departmental Service 2016 -To Present

(PhD Advanced Exam Committee for Rebekah Jones (12/2016), Abigail Richard (12/2016) and Hyogo Shibahara (TBA) ) Member Type:Departmental Service

(PhD Dissertation Committee for Rebekah Jones (04/2019), Abigail Richard (05/2019) and Hyogo Shibahara (TBA) ) Member Type:Departmental Service

National Science Centre (Poland) (External Grant Reviewer ) 03-2017

(Prelim Examination Committee (Real and Complex Analysis) ) Member Type:Departmental Service 2015 -2018

(Co-organizer (with Nageswari Shanmugalingam) of a special session on “Analysis and Geometry in Non-Smooth Spaces” at the AMS Spring Eastern Sectional Meeting 2018, Northeastern University, April 21-22, 2018 )

Cincy Math Circle Member Type:Community Service Level:Local 10-2017 -To Present

Journal d'Analyse Mathematique Peer Review/Referee

(Qualifying Exam Committee ) Member Type:Departmental Service 2017 -To Present

(Co-organizer (with Nageswari Shanmugalingam) of a Taft Research Seminar on Non-Smooth Analysis ) Type:Departmental Service 2019

Forum Mathematicum Peer Review/Referee 03-2018

(Co-organizer for a sectional meeting of the American Mathematical Society at the University of Cincinnati during April 17-18, 2021. ) Committee Member

(Applied for and awarded NSF funds to enable early career US mathematicians to attend the conference "Latest in Geometric Analysis" in Bedlewo, Poland during November 2019 )

(Grant Reviewer for the Simons Foundation ) 2019 -2019

(Prelim Examination Committee (Real Analysis) ) Committee Chair 2018 -To Present

09-2015 -To Present: American Mathematical Society

09-2015 -To Present: American Association of University Professors

REAL ANALYSIS

-MATH-1045 APPLIED CAL II Level:Undergraduate

-MATH-1061 CALCULUS I Level:Undergraduate

Geometric Analysis Level:Graduate

15-MATH-251 CALCULUS I Level:Undergraduate

-MATH-1062 CALCULUS II Level:Undergraduate

Advanced Calculus II Level:Both