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Research Topic B

Abstract of the proposed UNIPhD research project

The Deligne-Mumford compactified moduli space categorizes stable algebraic curves with marked points, crucial in algebraic geometry for intersection theory. Its cohomology ring, too intricate to explore entirely, leads us to focus on the more manageable tautological ring. This subring derives from natural geometric elements within the moduli space, generated by psi and kappa classes. The aim is to uncover all tautological relations among these generators.

Our project centers on conjectured tautological relations, potentially verifying the strong DR/DZ equivalence conjecture. This conjecture posits a deep connection between different integrable hierarchies within cohomological field theories (CohFTs). While verified for simpler CohFTs and specific Gromov-Witten theory cases, we seek to provide more evidence and potentially prove this equivalence. Furthermore, expanding the investigation to include generalizations, such as homotopy CohFTs, quantum and super hierarchies associated with a CohFT, opens up an exciting path for further development.

I was born in Malaysia and am currently a Ph.D. student in mathematics, specializing in arithmetic and complex algebraic geometry. Previously, I pursued my master’s degree in mathematical physics in France, working on cohomological field theory and Givental’s theory under the guidance of Prof Guido Carlet. My academic journey began with a bachelor’s degree in physics in Malaysia, where my focus was on the differential geometric structures of general relativity and cosmology. My interest has always revolved around the mathematical foundations that underpin modern theoretical physics. Currently, my research goal is to better comprehend the enigmatic relationship between enumerative geometry and integrable systems. It is an exciting topic to study as it offers powerful mathematical results as well as important implications for string theory and quantum gauge theory. Beyond intellectual interests, I enjoy group treks and playing sports, meeting people from diverse cultures, and attending retreats during my spare time.

Topic assigned to

Ishan Singh

Project documents.

• Research options for topic B

Doctoral Program in Mathematical Sciences

Corso di dottorato in scienze matematiche, recent theses (mathematics).

List of the PhD theses prepared within the Mathematics Curriculum in the last years. (The name of the supervisor is enclosed in brackets. Most of the theses can be downloaded from PaDUA@research , the Digital Archive of the University of Padova: just click on the thesis' title).

XXXII Cycle

• Davide Barco, A topological approach to the Fourier transform of an elementary D-module (Andrea D'Agnolo)
• Federico Campanini,  Weak forms of the Krull-Schmidt theorem and Prüfer rings in distinguished construction s (Alberto Facchni)
• Maria Teresa Chiri, Structural properties of solutions, approximation and control for conservation laws with discontinuous flux and bioinspired PDE models (Fabio Ancona)
• Giacomo Graziani, Modular sheaves of de Rham classes on Hilbert formal modular schemes for unramified primes (Adrian Iovita)
• Maria Giovanna Le Gros, Minimal approximations for cotorsion pairs generated by modules of projective dimension at most one over commutative rings (Silvana Bazzoni)
• Federico Venturelli, The Alexander polynomial of certain classes of non-symmetric line arrangements (Remke N. Kloosterman)
• Roberto Bramati, Geometric integral inequalities on homogeneous spaces (Paolo Ciatti)
• Sebastiano Don, Functions of bounded variation in Carnot-Carathéodory spaces (Davide Vittone)
• Simone Giovannini, On some examples in higher Auslander-Reiten theory (Silvana Bazzoni)
• Yan Hu, Rationality of darmon points over genus fields of nonmaximal orders (Matteo Longo)
• Paolo Luzzini, Regularizing properties of the double layer heat potential and shape analysis of a periodic proble m (Massimo Lanza de Cristoforis)
• Roman Pukhtaievych, Periodic and hypercomplex potentials. Properties and applications (Massimo Lanza de Cristoforis)
• Marco Tarantino, Recollements from exact model structures and heart constructions in triangulated categories (Silvana Bazzoni)
• Anna Tovo, Mathematical Modelling and Statistics of Biodiversity (Marco Favretti)
• Ferraresso Francesco, On the spectral stability of polyharmonic operators on singularly perturbed domains (Pier Domenico Lamberti)
• Aigul Myrzagaliyeva, On pointwise multipliers in some function spaces   (Massimo Lanza de Cristoforis)
• Leone Cesare Cimetta, Some properties of zeta functions associated to profinite groups (Andrea Lucchini)
• Laura Cossu, Factorizations of invertible matrices into products of elementary matrices and of singular matrices into products of idempotent matrices (Paolo Zanardo)
• Ismail Abdelsheed Gad Ameen, Fractional calculus: numerical methods and SIR models (Paolo Novati)

XXVIII Cycle

• Marta Zoppello, Controllability and optimization of deformable bodies in fluids: from biology to robotics (Franco Cardin)
• Luigi Provenzano, On mass distribution and concentration phenomena for linear elliptic partial differential operators (Pier Domenico Lamberti)
• Daria Ghilli, Some Results in Nonlinear PDEs: Large Deviations Problems, Nonlocal Operators, and Stability for Some Isoperimetric Problems (Martino Bardi)
• Valentina Franceschi, Sharp and Quantitative Isoperimetric Inequalities in Carnot-Carath é odory spaces (Roberto Monti)

XXVII Cycle

• Zhanar Taspaganbetova, Boundedness and compactness of matrix operators in weighted spaces of sequences and their applications (Massimo Lanza de Cristoforis)
• Guhanvenkat Harikumar, Darmon cycles and the Kohnen - Shintani lifting (Matteo Longo)
• Nguyen Khanh Tung, Cyclically presented modules, automorphism-invariant modules and poor modules (Alberto Facchini)
• Francesco Mattiello , New trends in tilting theory (Riccardo Colpi)
• Genaro Hernandez Mada, Monodromy Criterion for the Good Reduction of Surfaces (Bruno Chiarellotto )
• DavideBuoso, Shape sensitivity analysis of the eigenvalues of polyharmonic operators and elliptic systems (Pier Domenico Lamberti )
• Joao Henrique Branco Meireles, Singular Perturbations and Ergodic Problems for degenerate parabolic Bellman PDEs in R^m with Unbounded Data (Martino Bardi)
• Velibor Bojkovic, Finite morphism of p-adic curves (Francesco Baldassarri)
• Federico Bambozzi, On a generalization of affinoid varieties (Francesco Baldassarri)
• Marco Cirant, Nonlinear PDEs in ergodic control, Mean Field Games and prescribed curvature problems (Martino Bardi)
• Ly Kim Ha, On two approaches for partial differential equations in several complex variables (Giuseppe Zampieri)
• Nguyen Luong Van , On regular and singular points of the minimum time function (Giovanni Colombo)
• Dau The Phiet, Pseudoconvex domains: Diederich - Fornaess index and the invariant metrics near the boundary points (Giuseppe Zampieri)
• Martino Garonzi, Coverings of Groups by Subgroups (Andrea Lucchini)
• Alice Pavarin, Equivalences of additive categories (Silvana Bazzoni)
• Cecilia De Zan, Some new results on reaction-diffusion equations and geometric flows (Pierpaolo Soravia)
• Daniele Fontanari, Quantum manifestations of the adiabatic chaos of perturbed superintegrable Hamiltonian systems (Francesco Fassò, Dmitri í Sadovski í )
• Nicola Girardi, Regular biproduct decompositions of objects (Alberto Facchini)
• Nurgul Kydyrmina, Operators in Sobolev Morrey spaces (Viktor Burenkov)
• Paolo Musolino, Singular perturbation and homogenization problems in a periodically perforated domain. A functional analytic approach (Massimo Lanza de Cristoforis)
• Simone Vazzoler, Semiclassical limit: coherent states, quasimodes and WKB approximation (Franco Cardin)

XXIII Cycle

• Khai Tien Nguyen, The regularity of the minimum time function via nonsmooth analysis and geometric measure theory   (Giovanni Colombo)
• Gabriele Fusacchia, Injective modules over semistar Noetherian domains (Luigi Salce)
• Massimiliano Patassini, On the Dirichlet polynomial of the simple groups of Lie type (Andrea Lucchini)
• Marco Perone, Direct sum decompositions and weak Krull-Schmidt Theorems (Alberto Facchini)
• Valentina Settimi, On some additive problems with primes and powers of a fixed integer (Alessandro Languasco)
• Heer Zhao, On 1-Motives with torsion and their l-ADIC realisations (Barbieri Viale)
• Saltanat Rakhimova, The oscillation properties of half-linear second order and higher order differential equations (Ryskul Oinarov, Massimo Lanza de Cristoforis)
• Lyailya Zhapsarbayeva, Regularity and approximation properties of the solutions of second order degenerate and nonlinear elliptic systems (Otelbayev Mukhtarbay, Massimo Lanza de Cristoforis)
• Alice Ciccioni, On the Bloch-Ogus formalism for the rigid syntomic cohomology (Bruno Chiarellotto)
• Valentina Colombo, Some Properties Of The Moebius Function In The Subgroup Lattice Of The Alternating And Symmetric Groups (Andrea Lucchini)
• Raffaele Marigo, Separate analyticity and holomorphic sectors (Giuseppe Zampieri)
• Ermal Feleqi, Spectral stability estimates for the eigenfunctions of second order elliptic operators (Burenkov)
• Vu Khanh Tran, A general method of weights in the d-bar-Neumann problem (Giuseppe Zampieri)
• Crestani Eleonora, Monotone 2-Groups (Federico Menegazzo)
• Andrea Pavan, Computing Arithmetic Subgroups of Affine Algebraic Groups (Federico Menegazzo)
• Marco Formentin, Two problems concerning interacting systems: 1. On the purity of the free boundary condition Potts measure on Galton-Watson trees 2. Uniform propagation of chaos in some spin-flip models (Paolo Dai Prà)
• Matteo Dalla Riva, Potential theoretic methods for the analysis of singularly perturbed problems in linearized elasticity   (Massimo Lanza de Cristoforis)
• Giovanni Cerulli Irelli, Structural theory of rank three cluster algebras of affine type (Alberto Tonolo)
• Paola Zizzi, From Quantum Metalanguage to the Logic of Qubits (Giovanni Sambin, Pieralberto Marchetti)
• Gabriele Terrone, Singular Perturbation and Homogenization Problems in Control Theory, Differential Games and fully nonlinear Partial Differential Equations (Martino Bardi)
• Valentina Di Proietto, On p-adic differential equations on semistable varieties (Francesco Baldassarri)

Computational Mathematics, Learning, and Data Science 

Joint phd program unipv - usi - fbk.

2024 a dmission ( 40 ^o cycle) :  

call will be published on May 17 2024, see A dmission S ite

Computational Mathematics

Machine Learning, Deep Learning

Health Data Science and Statistical Learning

Computational Physics

Models, mathematics, statistics, data and algorithms are the foundations of our digital world. Computational methods and mathematical analysis are increasingly used for simulation, prediction, data evaluation, analysis, risk assessment, development and optimization, in virtually every field of Science.

The PhD in “ Computational Mathematics and Decision Sciences” aims at offering graduate students solid skills in Computational Mathematics, Computational Physics, Scientific Computing, Statistics, Optimization, Machine Learning, Data Sciences as well as an interdisciplinary view of Applied Mathematics, Physics and decision processes under uncertainty. The program gives a solid theoretical and computational grounding for high level research in universities, international research institutions and industry.

This international PhD program is organized jointly with the Euler Institute of the Universita` della Svizzera Italiana (USI) and the Fondazione Bruno Kessler (FBK). It is also a multidisciplinary PhD program with Faculty from the Departments of Mathematics, Physics, Political Sciences, Brain and Behavioral Sciences of UniPV and the Fondazione Mondino IRCCS, the IMATI-CNR Institute and the National Institute of Nuclear Physics (INFN).

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ATTENTION: during the week May 13 - 17, 2024, the PhD Office is closed to the public, due to moving from via Venezia 15 to via Martiri della Libertà 8, Padua.

The University of Padua coordinates 40 separate PhD Programmes; every year it welcomes between 500 and 600 new candidates, with approximately 1600 PhD candidates enrolled in a three/four-year degree programme. In order to apply for a PhD Course applicants must be in possession of a 2nd cycle degree (laurea magistrale or laurea magistrale a ciclo unico. They are also required to pass an entrance examination. An International PhD guide is now available: an handy tool to navigate your way around the University and live your experience to the fullest.

• The International PhD guide

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When the PhD path leads to career struggles

A doctoral degree is a major commitment. Think carefully.

I appreciated reading Kara Miller’s The Big Idea column “PhD: Pretty heavily disappointed” (Business, May 22), about people with doctoral degrees struggling to build careers in academia. It made me think back to a conversation I had when I was about to graduate from high school.

I happened to run into a former track coach of mine, and as we were reminiscing he asked me what I planned as a major in college. “History,” I responded. He said, “Why don’t you take some computer classes also? It never hurts to be able to do something useful.”

I did not reflect on his motivation at the time, but my track coach was a young guy, and he was probably giving me advice straight from his own life, as a parent trying to raise his own young children. I did take computer classes in college and ultimately received a PhD in chemical engineering. I always remember that conversation as being a kind of turning point.

Earning a doctoral degree is a life commitment of great proportion. It can take, as Miller notes, between four and seven years. If we think of working life as roughly between the ages of 22 and 65, then a PhD requires more than 10 percent of a person’s working life. People need to think carefully about that investment.

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Two powerful arguments in favor of the path of science, technology, engineering, and math are that there tend to be more STEM jobs for PhDs, and many universities’ STEM departments are generous in covering their PhD students’ tuition and cost of studies, including a stipend toward food, rent, and other expenses.

Stuart Gallant

Not much has changed in 30 years

As I prepared to graduate in 1995 with a doctor of education degree from the Harvard Graduate School of Education, my mother memorably said to me, “Of my four children, you are the one with the most education and the smallest salary.” Apparently not much has changed in 30 years.

I must congratulate these students, however, on following their passion rather than following the money. I can’t help but think that their lives, though stressful, may contain greater happiness.

Peggy Clark

Lawyers & electricians & philosophers, oh my!

Kara Miller’s column on the career challenges for people with doctoral degrees generated more than 260 comments on Boston.Globe.com. The following is an edited sample of readers’ reactions:

Lots of law school grads are underemployed as well. (PL)

So true, PL. The market in Massachusetts is flooded with talented lawyers seeking work. (Roforma)

Supply and demand, the market at work. (guk)

Investing in education and research in all fields is the hallmark of a society with staying power. Disinvesting from these endeavors signals decline and decay. (Massachusetts citizen)

Electricians, plumbers, mechanics, and other skilled technical professions have no problems getting $100k jobs with great benefits. (ramsen)

Not enough turnover from tenured professors, leaving little space for new faculty. Although the tenured, well-established professors are needed, it’s the junior faculty who are hungry and with new ideas that help build new programs. The whole graduate program model is a bad model. I worked two jobs, had my tuition and some type of minimal student health insurance and could barely cover the rent with my stipend, and the second job paid for everything else. Though I was working on many faculty projects, it was the faculty who said this would be good for me. Never did they say it was also good for them. (TravelerofNJ2)

I just retired from a tenured faculty position in science. I’m in my early 70s. I have colleagues who are still doing what they do well into their 70s, a couple approaching 80. There is no active incentive from the university to move the older faculty on, to make way for a new generation. (Lola-lola)

The next step is for adjuncts to go on strike across the nation and hold colleges and universities accountable. The current system is completely absurd. (Wordsmith2358)

Universities should be required to release disclosure data about the fate of their PhD graduates. (davidman820)

I knew an attorney who managed a Cheesecake Factory. She had worked in food services through school. As an attorney, she really did not make that much money and was not doing the field of law of her choice. How many real estate closings can you do without dying of boredom? She went into management in the food industry and makes the same salary. (Antietem)

It was always a question and puzzling to me why people study philosophy. (Blazer27)

Globe Opinion