phd maths unitn

Doctoral Students

Xxxix cycle - year 2023/2024.

• ANTOLINI Dario
• BARCELO' NIEVES Diego Alberto
• BELLETTINI Martina
• BERGANTIN Ester
• DAL MOLIN Luca
• DE BERNARDINI Daniele
• DE NARDI Alex
• DE ROSA Carmine
• FILIPPOZZI Lucia
• KARAPIPERI Christina
• LAUDENZI Bianca Maria
• MARQUIS Ulysse
• MORETI Stefan
• OUTALEB Youness
• PETTINARI Lorenzo
• SABBATINO MIchela
• STRAFFELINI Cesare
• ZAMBANINI Kilian

XXXVIII Cycle - Year 2022/2023

• BIZZOTTO Andrea
• CALDINI Gianmarco
• CAMPANILE Elio
• DALMASO Caterina
• DI BELLA Emanuele
• DI PETRILLO Gemma
• FILOSI Tobia
• LUISE Martina
• MARCHESIN Riccardo
• MAROTTA Angelo
• VIELMO Carlotta

XXXVII Cycle - Year 2021/2022

• ABRAM Valentino
• CAVICCHIONI Giulia
• DATRES Massimiliano
• DE BELLIS Alfredo
• FLAMINI Andrea
• FRACCAROLO Nicola
• FRAMBA  Matteo
• LOMBARDI Giulia
• MENEGALE Francesco
• MORSELLI Gabriele
• SANFILIPPO Anna
• SPADAFORA Chiara
• TOGNOLINI Giovanni
• VARDANYAN Viktorya
• VERZELLESI Simone
• ZAMPA Enrico

XXXVI Cycle - Year 2020/2021

• BARBAN Lorenzo
• BATTAGLIOLA Michele
• BINOSI Giulio
• BURIOLA Gabriele
• DEL ZOZZO Agnese
• FERRARESE Federica
• GALGANO Vincenzo
• GARBELLI Matteo
• LUCCA Alessia
• MOLINA GRANE Carla
• MULA Marzio
• SPILIMBERGO Alessandra
• TABARELLI Gloria
• VIANELLO Giacomo

XXXV Cycle - Year 2019/2020

• CARBONE Antonio
• CASSINI Fabio
• FALLUCCA Federico
• FOCHESATO Anna
• FRANCESCHINI Alberto
• GHITTI Beatrice
• MARESI Emiliano
• MORO Andrea
• MOSCATO Antonio
• PETIT VALDES Villarreal Paolo Eugenio
• SAVI Enrico
• SOTTILE Sara
• VOLPE Daniele

Doctoral School in Mathematics

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The complete list of publications of the members of the Department of Mathematics can be obtained from the archive Digital University of the University of Trento.

IRIS: repository of scientific publications and PhD thesis .

Unitn-eprints.PhD : repository of PhD thesis (until 2019).

Edge-colorings and flows in Class 2 graphs

Vai alla mappa

Tabarelli Gloria  - PhD in Mathematics, University of Trento

Abstract: We consider edge-colorings and flows problems in Graph Theory that are hard to solve for Class 2 graphs. Most of them are strongly related to some outstanding open conjectures, such as the Cycle Double Cover Conjecture, the Berge-Fulkerson Conjecture, the Petersen Coloring Conjecture and the Tutte's 5-flow Conjecture. We obtain some new restrictions on the structure of a possible minimum counterexample to the former two conjectures. We prove that the Petersen graph is, in a specific sense, the only graph that could appear in the statement of the Petersen Coloring Conjecture, and we provide evidence that led to propose an analogous of the Tutte's 5-flow conjecture in higher dimensions. We finally prove a characterization result and a sufficient condition for general graphs in relation to another edge-coloring problem, which is the determination of the palette index of a graph.

Valter Moretti

Coordinatore, corso di dottorato - matematica, professore ordinario, dipartimento di matematica.

Ph.D. Program Overview

Description.

The graduate program in the field of mathematics at Cornell leads to the Ph.D. degree, which takes most students five to six years of graduate study to complete. One feature that makes the program at Cornell particularly attractive is the broad range of  interests of the faculty . The department has outstanding groups in the areas of algebra, algebraic geometry,  analysis, applied mathematics, combinatorics, dynamical systems, geometry, logic, Lie groups, number theory, probability, and topology. The field also maintains close ties with distinguished graduate programs in the fields of  applied mathematics ,  computer science ,  operations research , and  statistics .

Core Courses

A normal course load for a beginning graduate student is three courses per term. 

There are no qualifying exams, but the program requires that all students pass four courses to be selected from the six core courses. First-year students are allowed to place out of some (possibly, all) of the core courses. In order to place out of a course, students should contact the faculty member who is teaching the course during the current academic year, and that faculty member will make a decision. The minimum passing grade for the core courses is B-; no grade is assigned for placing out of a core course.

At least two core courses should be taken (or placed out) by the end of the first year. At least four core courses should be taken (or placed out) by the end of the second year (cumulative). These time requirements can be waived for students with health problems or other significant non-academic problems. They can be also waived for students who take time-consuming courses in another area (for example, CS) and who have strong support from a faculty; requests from such students should be made before the beginning of the spring semester. 

The core courses  are distributed among three main areas: analysis, algebra and topology/geometry. A student must pass at least one course from each group. All entering graduate students are encouraged to eventually take all six core courses with the option of an S/U grade for two of them. 

The six core courses are:

MATH 6110, Real Analysis

MATH 6120, Complex Analysis

MATH 6310, Algebra 1

MATH 6320, Algebra 2

MATH 6510, Introductory Algebraic Topology

MATH 6520, Differentiable Manifolds.

Students who are not ready to take some of the core courses may take MATH 4130-4140, Introduction to Analysis, and/or MATH 4330-4340, Introduction to Algebra, which are the honors versions of our core undergraduate courses.

"What is...?" Seminar

The "What Is...?" Seminar is a series of talks given by faculty in the graduate field of Mathematics. Speakers are selected by an organizing committee of graduate students. The goal of the seminar is to aid students in finding advisors.

Schedule for the "What Is...?" seminar

Special Committee

The Cornell Graduate School requires that every student selects a special committee (in particular, a thesis adviser, who is the chair or the committee) by the end of the third semester.

The emphasis in the Graduate School at Cornell is on individualized instruction and training for independent investigation. There are very few formal requirements and each student develops a program in conjunction with his or her special committee, which consists of three faculty members, some of which may be chosen from outside the field of mathematics. 

Entering students are not assigned special committees. Such students may contact any of the members on the Advising Committee if they have questions or need advice.

Current Advising Committee

Analysis / Probability / Dynamical Systems / Logic: Lionel Levine Geometry / Topology / Combinatorics: Kathryn Mann Probability / Statistics:  Philippe Sosoe Applied Mathematics Liaison: Richard Rand

Admission to Candidacy

To be admitted formally to candidacy for the Ph.D. degree, the student must pass the oral admission to candidacy examination or A exam. This must be completed before the beginning of the student's fourth year. Upon passing the A exam, the student will be awarded (at his/her request) an M.S. degree without thesis.

The admission to candidacy examination is given to determine if the student is “ready to begin work on a thesis.” The content and methods of examination are agreed on by the student and his/her special committee before the examination. The student must be prepared to answer questions on the proposed area of research, and to pass the exam, he/she must demonstrate expertise beyond just mastery of basic mathematics covered in the core graduate courses. 

To receive an advanced degree a student must fulfill the residence requirements of the Graduate School. One unit of residence is granted for successful completion of one semester of full-time study, as judged by the chair of the special committee. The Ph.D. program requires a minimum of six residence units. This is not a difficult requirement to satisfy since the program generally takes five to six years to complete. A student who has done graduate work at another institution may petition to transfer residence credit but may not receive more than two such credits.

The candidate must write a thesis that represents creative work and contains original results in that area. The research is carried on independently by the candidate under the supervision of the chairperson of the special committee. By the time of the oral admission to candidacy examination, the candidate should have selected as chairperson of the committee the faculty member who will supervise the research. When the thesis is completed, the student presents his/her results at the thesis defense or B Exam. All doctoral students take a Final Examination (the B Exam, which is the oral defense of the dissertation) upon completion of all requirements for the degree, no earlier than one month before completion of the minimum registration requirement.

Masters Degree in the Minor Field

Ph.D. students in the field of mathematics may earn a Special Master's of Science in Computer Science. Interested students must apply to the Graduate School using a form available for this purpose. To be eligible for this degree, the student must have a member representing the minor field on the special committee and pass the A-exam in the major field. The rules and the specific requirements for each master's program are explained on the referenced page.

Cornell will award at most one master's degree to any student. In particular, a student awarded a master's degree in a minor field will not be eligible for a master's degree in the major field.

Graduate Student Funding

Funding commitments made at the time of admission to the Ph.D. program are typically for a period of five years. Support in the sixth year is available by application, as needed. Support in the seventh year is only available by request from an advisor, and dependent on the availability of teaching lines. Following a policy from the Cornell Graduate School, students who require more than seven years to complete their degree shall not be funded as teaching assistants after the 14th semester.

Special Requests

Students who have special requests should first discuss them with their Ph.D. advisor (or with a field member with whom they work, if they don't have an advisor yet). If the advisor (or field faculty) supports the request, then it should be sent to the Director of Graduate Studies.  

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Dept. of Department of Mathematics

Earn admissions to a nationally ranked program.

Incoming Ph.D. students are expected to pass  qualifying examinations  by the end of their third semester in the Ph.D. program.

After passing the qualifying examinations, students are expected to select a thesis adviser and form a doctoral committee. The committee administers the comprehensive examination (no later than the end of the sixth semester of study) and offers counsel to the student as his research progresses.

• No credit will be given for any course in which a grade of less than B is received.
• A minimum grade point average of 3.0 is required for graduation for all advanced degrees.

Requirements

• American English Oral Communicative Proficiency Test (AEOCPT)-International students only  ( Graduate School requirement) This exam must be taken upon arrival during the week of orientation. Students who pass the exam may teach without restrictions; marginal or failing students must register for the appropriate ESL course .  
• SARI/CITI (Scholarship and Research Integrity/Collaborative Institutional Training Initiative) ( Graduate School requirement ) The  SARI@PSU program is composed of two parts: an online course, and an interactive, discussion-based component; and encompasses content that is both interdisciplinary and discipline-specific. The online portion Part 1 ), offered through the Collaborative Institutional Training Initiative (CITI), provides a common language and understanding of the history and principles of the responsible conduct of research. This requirement must be completed within the first two weeks of the semester of arrival. The discussion-based component Part 2)provides an opportunity for in-depth exploration of important issues unique to each field of study. Part 2 is completed by attendance at the Graduate Student Seminar (see below).  
• Qualifying Examinations  ( Departmental requirement ) Ph.D. students are expected to pass four qualifying examinations out of the following areas: real analysis, linear algebra, abstract algebra, complex analysis, functional analysis, topology.  All students are required to pass real analysis and complex analysis. Students may then choose between linear and abstract algebra and functional analysis and topology.  Exams must be completed by the end of their third semester in the Ph.D. program. The system of qualifying examinations is explained in detail  here:  Qualifying Exams .  
• Colloquium Attendance Requirement  ( Departmental requirement ) Students year one (1) through the semester of the Ph.D. Oral Comprehensive Examination are required to attend at least 12 colloquium talks each academic year. Four (4) of the talks may be substituted by Departmental Seminars. First-year students (only) may substitute Student Colloquium talks for some of the required Departmental Colloquium talks. Students post-comprehensive are required to attend six (6) colloquium talks with NO substitutions.  Colloquium Attendance Form for 2023-24.  
• Graduate Student Seminar Requirement ( Departmental requirement ) This is a three credit course offered every spring. It is a requirement that every student successfully completes the seminar before his or her third year of study.  
• Ph.D. Candidacy  ( Graduate School requirement ) The Department of Mathematics will recommend Ph.D. candidacy after a student has passed all qualifying examinations and successfully completed 18 credits of Mathematics courses. Admission to candidacy is conferred by the Graduate School.  
• Oral and Written English Competency  ( Graduate School and Departmental requirement ) A candidate for the degree of Doctor of Philosophy is required to demonstrate high-level competence in the use of the English language, including reading, writing, and speaking, as part of the language and communication requirements for the Ph.D. Oral competency is assessed by the GTA (Graduate Teaching Assistant) Oversight Committee. Written competency is evaluated by the students' advisor. For additional detail, please see  Oral and Written English Competency .  
• Advisers and Doctoral Committees  ( Graduate School requirement ) Consultation or arrangement of the details of the student's semester-by-semester schedule is the function of the adviser. General guidance of a doctoral candidate is the responsibility of a doctoral committee consisting of four or more active members of the Graduate Faculty, which normally includes at least two faculty in the major field and is chaired by the student's adviser. This committee is appointed by the Graduate Dean through the Office of Graduate Programs, upon recommendation of the Director of Graduate Studies. A student should have an adviser by the end of their fourth semester and must have an adviser by the end of their fifth semester in the Ph.D. program.  
• Course Requirements  ( Departmental requirement ) Students must receive a minimum grade of B in at least eleven 3-credit 500-level mathematics courses. Students must take the Graduate Student Seminar before the third year of study.  

Starting 5/8/23:  All Modes Allowed The comprehensive examination may be held fully in-person, fully remote, or hybrid with some individuals participating in-person while others participate remotely. Student preference for delivery mode should be strongly considered, but the student and adviser must agree on the mode. If the student and adviser cannot agree on the mode, the Graduate Program Head will make the final decision. Either the student or adviser can appeal the decision of the Graduate Program Head to the ( insert appropriate graduate education administration role for the unit role, e.g. Associate Dean for Graduate Education, Director of Academic Affairs, etc. ).

• Ph.D. Thesis  ( Graduate School requirement ) The ability to do independent research and competence in scholarly exposition must be demonstrated by the preparation of a thesis on some topic related to the major subject. It should represent a significant contribution to knowledge, be presented in a scholarly manner, reveal an ability on the part of the candidate to do independent research of high quality, and indicate considerable experience in using a variety of research techniques. The contents and conclusions of the thesis must be defended at the time of the final oral examination. A draft of the thesis must be submitted to the doctoral committee a month before the final oral examination.  

Starting 5/8/23:  All Modes Allowed

The final oral examination (dissertation defense) may be held fully in-person, fully remote, or hybrid with some individuals participating in-person while others participate remotely.  Student preference for delivery mode should be strongly considered, but the student and adviser must agree on the mode. If the student and adviser cannot agree on the mode, the Graduate Program Head will make the final decision. Either the student or adviser can appeal the decision of the Graduate Program Head to the ( insert appropriate graduate education administration role for the unit role, e.g. Associate Dean for Graduate Education, Director of Academic Affairs, etc. ).

• Residency Requirement  ( Graduate School requirement ) After being admitted to candidacy, the student must be a full-time graduate student as defined by the Graduate Bulletin for two consecutive semesters (excluding summers) before comprehensive examinations can be scheduled.  
• Continuous Registration  ( Graduate School requirement ) After a Ph.D. candidate has passed the comprehensive examination and has met the two-semester full-time residency requirement (above), the student must register continuously for each fall and spring semester (beginning with the first semester after both of the above requirements have been met) until the Ph.D. thesis is accepted and approved by the doctoral committee.