Dr Murat Akman
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Email
murat.akman@essex.ac.uk -
Telephone
+44 (0) 1206 873032
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Location
STEM 5.12, Colchester Campus
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Academic support hours
Open Door Policy (subject to change when the term starts)
Profile
Biography
I am currently a senior lecturer at the University of Essex, UK. Before arriving to Essex, I was Evarist Giné Assistant Research Professor at the University of Connecticut and before that I was a postdoctoral researcher at the Instituto de Ciencias Matematicas, Madrid, Spain. I did my PhD at the University of Kentucky in 2014. I also received postdoctoral researcher fellowship from Institut Mittag-Leffler, Stockholm, Sweden to attend the Evolutionary Problems semester in the fall of 2013. During the spring semester of 2017, I was a postdoctoral fellow at the Mathematical Sciences Research Institute, Berkeley, CA to participate in the Harmonic Analysis program. You can find more information on my personal webpage: https://makmanx.github.io/. Google scholar page: https://scholar.google.com/citations?user=6wnq92oAAAAJ&hl=en. My research lies in the interface of harmonic analysis, elliptic and parabolic Partial Differential Equations, Potential Theory, and Geometric Measure Theory. In particular, I am interested in linear and nonlinear elliptic PDEs. My interests are - Variational methods for linear and quasi-linear elliptic and parabolic PDEs. - Regularity and free boundary regularity for linear and quasi-linear elliptic and parabolic PDEs in non-smooth domains. - Conformal densities and metric properties of harmonic, p-harmonic, and elliptic measures. - Brunn-Minkowski type inequalities associated to quasi-linear elliptic PDEs and stability of these inequalities. - Minkowski type problems associated to quasi-linear elliptic PDEs.
Qualifications
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PhD University of Kentucky, (2014)
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Bachelor of Science in Mathematics Middle East Technical University, (2006)
Appointments
University of Essex
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Lecturer, The Department of Mathematical Sciences, University of Essex (2/9/2019 - present)
Other academic
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Evarist Gine Assistant Research Professor, Department of Mathematics, University of Connecticut (23/8/2016 - 1/1/2017)
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Postdoctoral Researcher, Mathematical Sciences Research Institute (1/1/2017 - 26/5/2019)
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Evarist Gine Assistant Research Professor, Department of Mathematics, University of Connecticut (26/5/2017 - 1/7/2019)
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Postdoctoral researcher, Institute of Mathematical Sciences (15/10/2014 - 23/8/2016)
Research and professional activities
Research interests
Brunn-Minkowski type inequalities associated to quasi-linear elliptic PDEs and stability of these inequalities.
Minkowski type problems associated to quasi-linear elliptic PDEs.
Perturbation of elliptic operators on non-smooth domains
Regularity and free boundary regularity for quasi-linear elliptic PDEs in rough domains
Conformal densities and metric properties of measures
Conferences and presentations
Around the Minkowski problem and Brunn-Minkowski inequality
Invited presentation, Analysis seminar, Syracuse, United States, 27/5/2022
Perturbation of elliptic operators in 1-sided NTA domains satisfying the CDC
Invited presentation, Analysis Seminar, Knoxville, United States, 13/4/2022
Failure of Fatou type theorems for solutions to PDE of p-Laplace type in domains with flat boundaries
Invited presentation, The PDEs and Applications seminar, Uppsala, Sweden, 29/3/2022
Perturbation of elliptic operators in 1-sided NTA domains satisfying the capacity density condition.
Invited presentation, Interactions between Geometric measure theory, Singular integrals, and PDE, Interactions between Geometric measure theory, Singular integrals, and PDE, 17/3/2022
On the Brunn-Minkowski Inequality
Invited presentation, Keynote presentation, London Mathematical Society Harmonic Analysis and PDE Research Network, Canterbury, United Kingdom, 14/12/2021
A comparison of the UK and the US academic job markets for mathematicians.
Invited presentation, Keynote presentation, University of Kentucky Mathematics Alumni Week, Lexington, United States, 31/3/2021
On a Theorem of Wolff Revisited
Invited presentation, [Online] Graduate seminar on Advanced topics in PDE, Bonn, Germany, 12/6/2020
Gap series for p-harmonic functions
Invited presentation, 13th AIMS conference on Dynamical Systems, Differential Equations and Applications, 13th AIMS conference on Dynamical Systems, Differential Equations and Applications, Atlanta, United States, 5/6/2020
A Minkowski Problem and the Brunn-Minkowski Inequality for capacity
Invited presentation, Partial Differential Equations Seminar at University of Oxford, 9/3/2020
Perturbation of elliptic operators on rough domains
Invited presentation, Congreso de Jóvenes Investigadores de la RSME, Congreso de Jóvenes Investigadores de la RSME, Castelló de la Plana, Spain, 31/1/2020
Perturbation of elliptic operators on rough domains
Invited presentation, Analysis Seminar at University of Birmingham, 10/12/2019
A Minkowski problem for nonlinear capacity
Invited presentation, Kent Analysis Seminar, 10/10/2019
Teaching and supervision
Current teaching responsibilities
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Real Analysis (MA203)
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Complex Variables (MA302)
Publications
Journal articles (16)
Akman, M. and Mukherjee, S., (2024). On the Minkowski problem for p-harmonic measures. Calculus of Variations and Partial Differential Equations. 64 (1)
Akman, M., Banerjee, A. and Munive, IH., (2023). Borderline gradient continuity for the normalized p-parabolic operator. Journal of Geometric Analysis. 33 (8)
Akman, M., Hofmann, S., Martell, JM. and Toro, T., (2023). Perturbation of elliptic operators in 1-sided NTA domains satisfying the capacity density condition. Forum Mathematicum. 35 (1), 245-295
Akman, M., Hofmann, S., Martell, JM. and Toro, T., (2022). Square function and non-tangential maximal function estimates for elliptic operators in 1-sided NTA domains satisfying the capacity density condition. Advances in Calculus of Variations. 16 (3), 731-766
Akman, M., Lewis, J., Saari, O. and Vogel, A., (2021). The Brunn-Minkowski inequality and a Minkowski problem for A-harmonic Green's function. Advances in Calculus of Variations. 14 (2), 247-302
Akman, M., Banerjee, A. and Smit Vega Garcia, M., (2021). On a Bernoulli-type overdetermined free boundary problem. Annales Fennici Mathematici. 46 (2), 601-618
Akman, M., Lewis, J. and Vogel, A., (2020). Note on an eigenvalue problem with applications to a Minkowski type regularity problem in $\Bbb R^n$. Calculus of Variations and Partial Differential Equations. 59 (2), Paper No. 47-36
Akman, M., Lewis, J. and Vogel, A., (2020). Note on an eigenvalue problem for an ODE originating from a homogeneous $p$-harmonic function. St. Petersburg Mathematical Journal. 31 (2), 241-250
Akman, M., Azzam, J. and Mourgoglou, M., (2019). Absolute continuity of harmonic measure for domains with lower regular boundaries. Advances in Mathematics. 345, 1206-1252
Akman, M., Badger, M., Hofmann, S. and Martell, JM., (2019). Rectifiability and elliptic measures on 1-sided NTA domains with Ahlfors-David regular boundaries. Transactions of the American Mathematical Society. 369 (8), 5711-5745
Akman, M., Bortz, S., Hofmann, S. and Martell, JM., (2019). Rectifiability, interior approximation and Harmonic measure. Arkiv för Matematik. 57 (1), 1-22
Akman, M., Lewis, J. and Vogel, A., (2017). σ-Finiteness of elliptic measures for quasilinear elliptic PDE in space. Advances in Mathematics. 309, 512-557
Akman, M., (2016). On the absolute continuity of p-harmonic measure and surface measure in Reifenberg flat domains. Pacific Journal of Mathematics. 286 (1), 25-37
Akman, M., Lewis, J. and Vogel, A., (2015). Hausdorff dimension and σ finiteness of p harmonic measures in space when p ≥ n. Nonlinear Analysis: Theory, Methods and Applications. 129, 198-216
Akman, M., (2014). On the dimension of a certain Borel measure in the plane. Annales Academiae Scientiarum Fennicae. Mathematica. 39 (1), 187-209
Akman, M., Lewis, JL. and Vogel, A., (2012). On the logarithm of the minimizing integrand for certain variational problems in two dimensions. Analysis and Mathematical Physics. 2 (1), 79-88
Books (1)
Akman, M., Gong, J., Hineman, J., Lewis, J. and Vogel, A., (2022). The Brunn-Minkowski inequality and a Minkowski problem for nonlinear capacity. American Mathematical Society (AMS)
Thesis dissertation (1)
Akman, M., (2014). On the Hausdorff dimension of a certain measure arising from a positive weak solution to a divergence type PDE
Grants and funding
2022
Stability of Brunn-Minkowski inequalities and Minkowski type problems for nonlinear capacity
Engineering and Physical Sciences Research Council
2020
Integrability and Analysis of PDEs (Day 2)
London Mathematical Society
Contact
Academic support hours:
Open Door Policy (subject to change when the term starts)
