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Trosolwyg
Rwy'n Gadeirydd mewn Mathemateg ym Mhrifysgol Caerdydd ers mis Awst 2021.
Rwy'n aelod o'r Grŵp Dadansoddi a'r Grŵp Prosesau Dadansoddi, Tebygolrwydd a Stochastig.
Mae fy niddordebau ymchwil yn bennaf ym maes PDE aflinol , gan ddefnyddio technegau dadansoddi croesfannau, geometreg a dadansoddi stocastig. Yn benodol, rwy'n gweithio ar PDEs geometrig, sy'n gysylltiedig â grŵp Heisenberg, grwpiau Carnot a geometregau is-Riemannian cyffredinol.
Rolau Ysgol
- Uwch Diwtor
Rolau Eraill
- Arweinydd Node Cymru ar gyfer Atebion Cyffredinol a Rheoleidd-dra Isel EPSRC Rhwydwaith PDEs aflinol
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Aelod o banel EPSRC
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Bwrdd Bwrsariaethau Ymchwil Israddedigion LSM
Trefniadaeth y Gynhadledd, y gweithdy a'r Rhwydwaith Ymchwil
- Ysgol Haf mewn PDEs aflinol, Abertawe, Gorffennaf 2024
- Dulliau amrywiol ar gyfer PDEs aflinol, Caerdydd, Gorffennaf 2023
- Gweithdy ar Hafaliadau Aflinol: o theori i fodelu, Caerdydd, Tachwedd 2022
- Gweithdy ar Calculus o Amrywiad a PDE Nonlinear, Caerdydd, Ebrill 2022
- 12fed Rhwydwaith LMS Worhshop, Caerdydd, Tachwedd 2018
- Rhwydwaith 11eg LMS Worhshop, Caerdydd, Mai 2018
- 8fed Rhwydwaith LMS Worhshop, Caerdydd, Medi 2017
- Tueddiadau Newydd mewn PDE aflinol: o theori i geisiadau, Caerdydd, Mawrth 2016
- 2il Rhwydwaith LMS Worhshop, Caerdydd, Ebrill 2016
- Dulliau stochastig a PDE aflinol, Caerdydd, 2012
Gweithgareddau allgymorth
- Clybiau Gemau Mathemateg yn Llyfrgell Caerffili a Llyfrgell Bargod mewn cydweithrediad â CTG - Caerphilly Table-Top & Gamers Society
Cysylltiadau Allanol
Cyhoeddiad
2025
- Dragoni, F., Liu, Q. and Zhang, Y. 2025. Horizontal semiconcavity for the square of Carnot–Carathéodory distance on step 2 Carnot groups and applications to Hamilton–Jacobi equations. Nonlinearity 38, article number: 45009. (10.1088/1361-6544/adb930)
2024
- Citti, G., Dirr, N., Dragoni, F. and Grande, R. 2024. Horizontal mean curvature flow as a scaling limit of a mean field equation in the Heisenberg group. [Online]. arXiv: Cornell University. Available at: https://arxiv.org/abs/2411.15814
- Dragoni, F., Liu, Q. and Zhang, Y. 2024. Horizontal semiconcavity for the square of Carnot-Carathéodory distance on step 2 Carnot groups and applications to Hamilton-Jacobi equations. [Online]. arXiv. (10.48550/arXiv.2402.19164) Available at: https://doi.org/10.48550/arXiv.2402.19164
- Dragoni, F., Garofalo, N., Giovannardi, G. and Salani, P. 2024. A fundamental solution for a subelliptic operator in finsler geometry. [Online]. arXiv: Cornell University. (10.48550/arXiv.2401.06736) Available at: https://doi.org/10.48550/arXiv.2401.06736
- Dragoni, F. 2024. Semiconcavity, viscosity solutions and the square distance in Carnot groups.. Presented at: Summer School Workshop IV, Ghent, November 2024.
2021
- Dirr, N., Dragoni, F. and Grande, R. 2021. Asymptotics for optimal controls for horizontal mean curvature flow. Nonlinear Analysis 202, article number: 112076. (10.1016/j.na.2020.112076)
2020
- Dirr, N., Dragoni, F., Mannucci, P. and Marchi, C. 2020. Gamma-convergence and homogenisation for a class of degenerate functionals. Nonlinear Analysis 190, article number: 111618. (10.1016/j.na.2019.111618)
- Dirr, N., Dragoni, F. and Grande, R. 2020. Asymptotics for optimal controls for horizontal mean curvature flow.. [Online]. arXiv. Available at: https://arxiv.org/abs/2005.10599
2019
- Dragoni, F. and Filali, D. 2019. Starshaped and convex sets in Carnot groups and in the geometries of vector fields. Journal of Convex Analysis 4(24), pp. -.
- Dragoni, F., Garofalo, N. and Salani, P. 2019. Starshapedeness for fully non-linear equations in Carnot groups. Journal of the London Mathematical Society 99(3), pp. 901-918. (10.1112/jlms.12198)
2018
- Dirr, N., Dragoni, F., Mannucci, P. and Marchi, C. 2018. Stochastic homogenization for functionals with anisotropic rescaling and noncoercive Hamilton--Jacobi equations. SIAM Journal on Mathematical Analysis 50(5), pp. 5198-5242. (10.1137/17M1144428)
- Dragoni, F. and Feleqi, E. 2018. Ergodic mean field games with Hörmander diffusions. Calculus of Variations and Partial Differential Equations 57, article number: 116. (10.1007/s00526-018-1391-1)
2014
- Bardi, M. and Dragoni, F. 2014. Subdifferential and properties of convex functions with respect to vector fields. Journal of Convex Analysis 21(3), pp. 785-810.
2013
- Dragoni, F., Manfredi, J. J. and Vittone, D. 2013. Weak Fubini property and infinity harmonic functions in Riemannian and sub-Riemannian manifolds. Transactions of the American Mathematical Society 365, pp. 837-859. (10.1090/S0002-9947-2012-05612-1)
2012
- Dragoni, F., Kontis, V. and Zegarliński, B. 2012. Ergodicity of Markov semigroups with Hörmander type generators in infinite dimensions. Potential Analysis 37(3), pp. 199-227. (10.1007/s11118-011-9253-x)
2011
- Bardi, M. and Dragoni, F. 2011. Convexity and semiconvexity along vector fields. Calculus of Variations and Partial Differential Equations 42(3-4), pp. 405-427. (10.1007/s00526-011-0392-0)
- Gentil, I., Qian, Z., Roberto, C., Dragoni, F., Inglis, J. and Kontis, V. Zegarlinski, B. ed. 2011. Aspects of analysis curvature criterion, isoperimetry, evolution equations. Mathematical Notebooks Vol. 3. Matrix Press.
2010
- Dirr, N. P., Dragoni, F. and Von Renesse, M. 2010. Evolution by mean curvature flow in sub-Riemannian geometries: a stochastic approach. Communications on Pure and Applied Analysis 9(2), pp. 307-326. (10.3934/cpaa.2010.9.307)
- Bardi, M. and Dragoni, F. 2010. Convexity along vector fields and applications to equations of Monge-Ampére type. In: Ruzhansky, M. and Wirth, J. eds. Progress in Analysis and Its Applications. Proceedings of the 7th international ISAAC Congress.. World Scientific, (10.1142/9789814313179_0059)
2009
- Bieske, T., Dragoni, F. and Manfredi, J. J. 2009. The Carnot-Carathéodory Distance and the Infinite Laplacian. Journal of Geometric Analysis 19(4), pp. 737-754. (10.1007/s12220-009-9087-6)
2007
- Dragoni, F. 2007. Metric Hopf-Lax formula with semicontinuous data. Discrete and Continuous Dynamical Systems 17(4), pp. 713-729. (10.3934/dcds.2007.17.713)
- Dragoni, F. 2007. Limiting behavior of solutions of subelliptic heat equations. Nonlinear Differential Equations and Application NoDEA 14(3-4), pp. 429-441. (10.1007/s00030-007-6013-0)
2006
- Dragoni, F. 2006. Carnot-Carathéodory metrics and viscosity solutions. PhD Thesis, Scuola Normale Superiore, Pisa, Italy.
2005
- Barletti, L. and Dragoni, F. 2005. An inverse problem for two-frequency photon transport in a slab. Mathematical Methods in the Applied Sciences 28(14), pp. 1695-1714. (10.1002/mma.633)
Articles
- Dragoni, F., Liu, Q. and Zhang, Y. 2025. Horizontal semiconcavity for the square of Carnot–Carathéodory distance on step 2 Carnot groups and applications to Hamilton–Jacobi equations. Nonlinearity 38, article number: 45009. (10.1088/1361-6544/adb930)
- Dirr, N., Dragoni, F. and Grande, R. 2021. Asymptotics for optimal controls for horizontal mean curvature flow. Nonlinear Analysis 202, article number: 112076. (10.1016/j.na.2020.112076)
- Dirr, N., Dragoni, F., Mannucci, P. and Marchi, C. 2020. Gamma-convergence and homogenisation for a class of degenerate functionals. Nonlinear Analysis 190, article number: 111618. (10.1016/j.na.2019.111618)
- Dragoni, F. and Filali, D. 2019. Starshaped and convex sets in Carnot groups and in the geometries of vector fields. Journal of Convex Analysis 4(24), pp. -.
- Dragoni, F., Garofalo, N. and Salani, P. 2019. Starshapedeness for fully non-linear equations in Carnot groups. Journal of the London Mathematical Society 99(3), pp. 901-918. (10.1112/jlms.12198)
- Dirr, N., Dragoni, F., Mannucci, P. and Marchi, C. 2018. Stochastic homogenization for functionals with anisotropic rescaling and noncoercive Hamilton--Jacobi equations. SIAM Journal on Mathematical Analysis 50(5), pp. 5198-5242. (10.1137/17M1144428)
- Dragoni, F. and Feleqi, E. 2018. Ergodic mean field games with Hörmander diffusions. Calculus of Variations and Partial Differential Equations 57, article number: 116. (10.1007/s00526-018-1391-1)
- Bardi, M. and Dragoni, F. 2014. Subdifferential and properties of convex functions with respect to vector fields. Journal of Convex Analysis 21(3), pp. 785-810.
- Dragoni, F., Manfredi, J. J. and Vittone, D. 2013. Weak Fubini property and infinity harmonic functions in Riemannian and sub-Riemannian manifolds. Transactions of the American Mathematical Society 365, pp. 837-859. (10.1090/S0002-9947-2012-05612-1)
- Dragoni, F., Kontis, V. and Zegarliński, B. 2012. Ergodicity of Markov semigroups with Hörmander type generators in infinite dimensions. Potential Analysis 37(3), pp. 199-227. (10.1007/s11118-011-9253-x)
- Bardi, M. and Dragoni, F. 2011. Convexity and semiconvexity along vector fields. Calculus of Variations and Partial Differential Equations 42(3-4), pp. 405-427. (10.1007/s00526-011-0392-0)
- Dirr, N. P., Dragoni, F. and Von Renesse, M. 2010. Evolution by mean curvature flow in sub-Riemannian geometries: a stochastic approach. Communications on Pure and Applied Analysis 9(2), pp. 307-326. (10.3934/cpaa.2010.9.307)
- Bieske, T., Dragoni, F. and Manfredi, J. J. 2009. The Carnot-Carathéodory Distance and the Infinite Laplacian. Journal of Geometric Analysis 19(4), pp. 737-754. (10.1007/s12220-009-9087-6)
- Dragoni, F. 2007. Metric Hopf-Lax formula with semicontinuous data. Discrete and Continuous Dynamical Systems 17(4), pp. 713-729. (10.3934/dcds.2007.17.713)
- Dragoni, F. 2007. Limiting behavior of solutions of subelliptic heat equations. Nonlinear Differential Equations and Application NoDEA 14(3-4), pp. 429-441. (10.1007/s00030-007-6013-0)
- Barletti, L. and Dragoni, F. 2005. An inverse problem for two-frequency photon transport in a slab. Mathematical Methods in the Applied Sciences 28(14), pp. 1695-1714. (10.1002/mma.633)
Book sections
- Bardi, M. and Dragoni, F. 2010. Convexity along vector fields and applications to equations of Monge-Ampére type. In: Ruzhansky, M. and Wirth, J. eds. Progress in Analysis and Its Applications. Proceedings of the 7th international ISAAC Congress.. World Scientific, (10.1142/9789814313179_0059)
Books
- Gentil, I., Qian, Z., Roberto, C., Dragoni, F., Inglis, J. and Kontis, V. Zegarlinski, B. ed. 2011. Aspects of analysis curvature criterion, isoperimetry, evolution equations. Mathematical Notebooks Vol. 3. Matrix Press.
Conferences
- Dragoni, F. 2024. Semiconcavity, viscosity solutions and the square distance in Carnot groups.. Presented at: Summer School Workshop IV, Ghent, November 2024.
Thesis
- Dragoni, F. 2006. Carnot-Carathéodory metrics and viscosity solutions. PhD Thesis, Scuola Normale Superiore, Pisa, Italy.
Websites
- Citti, G., Dirr, N., Dragoni, F. and Grande, R. 2024. Horizontal mean curvature flow as a scaling limit of a mean field equation in the Heisenberg group. [Online]. arXiv: Cornell University. Available at: https://arxiv.org/abs/2411.15814
- Dragoni, F., Liu, Q. and Zhang, Y. 2024. Horizontal semiconcavity for the square of Carnot-Carathéodory distance on step 2 Carnot groups and applications to Hamilton-Jacobi equations. [Online]. arXiv. (10.48550/arXiv.2402.19164) Available at: https://doi.org/10.48550/arXiv.2402.19164
- Dragoni, F., Garofalo, N., Giovannardi, G. and Salani, P. 2024. A fundamental solution for a subelliptic operator in finsler geometry. [Online]. arXiv: Cornell University. (10.48550/arXiv.2401.06736) Available at: https://doi.org/10.48550/arXiv.2401.06736
- Dirr, N., Dragoni, F. and Grande, R. 2020. Asymptotics for optimal controls for horizontal mean curvature flow.. [Online]. arXiv. Available at: https://arxiv.org/abs/2005.10599
Ymchwil
Diddordebau ymchwil
Mae fy ymchwil yn cael ei ysgogi gan ystod eang o broblemau cydberthynol ym maes dadansoddi mewn maniffoldiau is-Riemannian ac yn dirywio PDE aflinol. Yn y lleoliadau hyn, rwyf wedi delio â chwestiynau gwahanol iawn, gan ddefnyddio llawer o ddulliau a thechnegau rhyngddisgyblaethol o debygolrwydd, dadansoddi, geometreg wahaniaethol, algebras Lie, gofodau metrig, calcwlws amrywiadau a theori mesur. Mae geometregau Is-Riemannian a PDEs cysylltiedig (fel PDE subelliptic/ultraparabolig) yn hynod ddefnyddiol i greu modelau mathemategol i ddisgrifio llawer o ffenomenau gwahanol o geisiadau. Enghraifft yw'r defnydd o'r geometreg Rototranslation ar gyfer modelu haen gyntaf y cortex gweledol a phroblemau mewn cyllid sy'n gysylltiedig â phrisio opsiynau Asiaidd fel y'u gelwir. Yn wahanol i maniffoldiau Riemannian (lle mae'r strwythur yn edrych yn lleol bob amser fel yr Ewclidaidd RN), nid yw gofodau is-Riemannian byth, ar unrhyw raddfa, yn isomorffig i'r gofod Ewclidaidd. Yn benodol, maent yn hynod anisotropig yn yr ystyr bod rhai cyfeiriadau ar gyfer y cynnig ar y manifold yn troi allan i gael eu gwahardd ar unrhyw adeg, gan wneud y strwythur metrig a geometrig yn llawer mwy cymhleth nag yn yr achos nad yw'n dirywio (gofod Ewclidaidd a manifolds Riemannian). Mae'r cyfarwyddiadau a ganiateir ar gyfer y cynnig yn cael eu disgrifio gan gaeau fector nad ydynt yn rhychwantu ar unrhyw adeg y gofod tangiad cyfan. Diffinnir PDEs ar y geometregau hyn trwy ddisodli'r deilliadau rhannol safonol gan y meysydd fector.
Mae rhai o'r pynciau sydd o ddiddordeb i mi wedi'u rhestru isod.
- PDEs aflinol, yn enwedig dirywio elipitic a PDEs parabolig.
- PDEs yn grwpiau Heisenberg a grwpiau Carnot
- PDEs mewn maniffoldiau is-Riemannian ac yn gyffredinol yn gysylltiedig â meysydd fector Hoermander
- Eiddo geometrig ar gyfer PDEs
- Convexity a starshapedness mewn mannau nad ydynt yn Ewclidaidd
- Dulliau stocastig ar gyfer PDE penderfynol
- Homogenization stocastig
- Hafaliadau Hamilton-Jacobi a fformiwlâu Hopf-Lax
- Hollol Minimizing estyniadau Lipschitz
- Anfeidrol-Laplacian
- Gemau Maes Cymedrig
- Tug-of-rhyfel, yn fwy mewn gemau gwahaniaethol penderfynol cyffredinol a stocastig
Grŵp ymchwil
Cyllid a grantiau allanol
- 2023-2024: Cynllun LMS 4; Absenoldeb Ymchwil Prifysgol Caerdydd
- 2020-2024: Node Cymru ar gyfer Rhwydwaith EPSRC ar Atebion Cyffredinol a Rheoleidd-dra Isel ar gyfer PDE Nonlinear
- 2019-2020: Grant Symudedd ERASMUS; Cronfeydd CU i ymweld Campinas
- 2018-2019: Cynllun 5 LMS (Cydweithio â gwledydd sy'n datblygu)
- 2017-2018: Absenoldeb Ymchwil Prifysgol Caerdydd; Cynllun LMS 3; Grant Addysg LMS
- 2016-2017: Cynllun Grant LMS 4; Cynllun Grant LMS 3
- 2015-2016: Grant Cyntaf EPSRC; Cynllun Grant LMS 3
- 2012-2013: Cynllun grant LMS 1; Grant oxPDE ar gyfer cynhadledd; Grant WIMCS ar gyfer cynhadledd
- 2010: Grant bach cydweithredol LMS
- 2007: Grant ymchwil INDAM
Addysgu
Ar hyn o bryd rwy'n dysgu'r modiwlau canlynol:
- MA20006 Dadansoddiad Gwirioneddol (Tymor y Gwanwyn)
Profiad blaenorol o addysgu
- Dadansoddiad go iawn. Blwyddyn 2, Caerdydd (2021-presennol)
- Pynciau pellach mewn Dadansoddi gyda cheisiadau i PDEs, Ôl-raddedig a chwrs MMath, Prifysgol Caerdydd (2016-2023)
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Sylfaen II, blwyddyn 1, Caerdydd (2016-2020)
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Dadansoddiad 2, blwyddyn 1, Caerdydd (2012, 2014, 2015)
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PDEs damcaniaethol a chyfrifiannol, blwyddyn 3, Caerdydd (2012, 2013)
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Algebra llinol, blwyddyn 1, Prifysgol Bryste (2010)
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Calculus 2, blwyddyn 1, Prifysgol Bryste (2010)
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Cyflwyniad i theori gludedd ar gyfer PDEs Nonlinearol, Ôl-raddedig a MMath, Coleg Imperial Llundain (2009)
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Calculus I a Geometreg ac Algebra llinol (cynorthwy-ydd addysgu), blwyddyn 1, Adran Peirianneg, Prifysgol Florence (2007)
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Dosbarth paratoadol o Fathemateg, Prifysgol Florence (2006)
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Mathemateg a Ffiseg mewn Ysgolion Uwchradd, Fflorens (2006)
Bywgraffiad
Addysg a Chymhwyster
- 2013: Cymrawd yr Academi Addysg Uwch (FHEA), Prifysgol Caerdydd.
- 2006: PhD mewn Mathemateg, Scuola Normale Superiore di Pisa, Yr Eidal. Marc: 70/70 cum Laude. Teitl: metrigau Carnot-Carathéodory ac atebion gludedd. Cynghorydd: Yr Athro Italo Capuzzo Dolcetta.
- 2002: Laurea (cyfwerth â Gradd Meistr) mewn Mathemateg, Prifysgol Fflorens, yr Eidal. Marc: 110/110 cum Laude. Teitl: Photon trafnidiaeth mewn cwmwl rhyngserol: problemau uniongyrchol a gwrthdro. Cynghorydd: Yr Athro Luigi Barletti
Cyflogaeth
- 2021-presennol: Cadwyn mewn Mathemateg yn Ysgol Mathemateg Caerdydd, Prifysgol Caerdydd
- 2016-2021: Uwch Ddarlithydd a'r Darllenydd yn Ysgol Mathemateg Caerdydd, Prifysgol Caerdydd
- 2011-2016: Darlithydd yn Ysgol Mathemateg Caerdydd, (gan gynnwys dau doriad o absenoldeb mamolaeth yn 2011 a 2013)
- 2010: Cydymaith ymchwil ym Mhrifysgol Padova, yr Eidal a swydd dros dro, Prifysgol Bryste
- 2009: Cydymaith Ymchwil yng Ngholeg Imperial Llundain
- 2008-2009: Cydymaith ymchwil ym Mhrifysgol Padova, yr Eidal
- 2007-2008: Sefyllfa ôl-doc yn Sefydliad Max Planck ar gyfer Mathemateg yn y Gwyddorau, Leipzig, Yr Almaen
- 2007: Sefyllfa ymchwil INDAM, ym Mhrifysgol Pittsburgh, UDA
Meysydd goruchwyliaeth
- Mae PDEs aflinol yn dirywio eliptig a pharabolic.
- PDEs mewn grwpiau Carnot, manifolds SubRiemannian ac yn gysylltiedig â meysydd fector Hoermander.
- Priodweddau geometrig ar gyfer PDEs.
- Convexity mewn mannau nad ydynt yn Ewclidaidd.
- Homogenization Cyfnodol
- Homogenizitaion stochastig
- Gemau Maes Cymedrig
Goruchwyliaeth gyfredol
Contact Details
DragoniF@caerdydd.ac.uk
+44 29208 75529
Abacws, Ystafell 2.19, Ffordd Senghennydd, Cathays, Caerdydd, CF24 4AG
+44 29208 75529
Abacws, Ystafell 2.19, Ffordd Senghennydd, Cathays, Caerdydd, CF24 4AG
