I am a third year PhD student under the supervision of Dr Adam HarperLink opens in a new window.

Email: Daniele "dot" Mastrostefano "at" warwick "dot" ac "dot'' uk.

Office: B0.16.

Research Interests:

The distribution of prime numbers, Additive and Multiplicative Number Theory, the elementary approach to Analytic Number Theory, the distribution of arithmetical functions, Sieve Theory, Additive Combinatorics, Probabilistic Number Theory and Metric Number Theory.

Publications and preprints:

• An almost sure upper bound for random multiplicative functions on integers with a large prime factorLink opens in a new window (Preprint).
• A lower bound for the variance in arithmetic progressions of some multiplicative functions close to 1Link opens in a new window (ArXiv preprint).
• The number of representations of an integer as product of two restricted numbersLink opens in a new window (Note).
• On maximal product sets of random setsLink opens in a new window (Published, The Journal of Number Theory).
• A lower bound for the variance of generalized divisor functions in arithmetic progressionsLink opens in a new window (Published, The Ramanujan Journal).
• Positive proportion of short intervals containing a prescribed number of primesLink opens in a new window (Published, Bulletin of Australian Mathematical Society).
• An Upper Bound for the Moments of a G.C.D. related to Lucas SequencesLink opens in a new window (Published, Rocky Mountain Journal of Mathematics).
• On numbers n with polynomial image coprime with the n-th term of a linear recurrenceLink opens in a new window (Published, Bulletin of the Australian Mathematical Society).
• Short intervals containing a prescribed number of primesLink opens in a new window (Published, Journal of Number Theory).
• Weighted Average Number of Prime m-tuples lying on an Admissible k-tuple of Linear FormsLink opens in a new window (Preprint, arXiv version).

Current Research:

This is my main PhD project.Link opens in a new window I am also working on understanding large fluctuations of random multiplicative functions together with Adam Harper.

Teaching:

I have been TA for the modules:

• MA257 Introduction to Number Theory (Second term 2019/2020).
• MA258 Mathematical Analysis IIILink opens in a new window (First term 2019/2020).
• MA257 Introduction to Number TheoryLink opens in a new window (Second term 2018/2019).
• MA258 Mathematical Analysis IIILink opens in a new window (First term 2018/2019).

I have been a supervisor for 2 groups of 5 each second year undergraduate students for the modules:

• MA244 Analysis 3Link opens in a new window (First term 2018/2019).
• MA251 Algebra 1: Advanced Linear AlgebraLink opens in a new window (First term 2018/2019).
• MA259 Multivariable CalculusLink opens in a new window (First term 2018/2019).

Activities:

• I gave a talk on my paper about "random multiplicative functions" during the SSANT, held in Paris (02 July 2021). Here is the video: https://archive.org/details/talk-SSANT2021-Mastrostefano.
• I gave a talk on ''Maximal random product sets'' during the Junior Number Theory seminar, virtually held in Oxford (3 May 2021).
• I gave a talk on "The variance of generalized divisor functions and other sequences in arithmetic
  progressions" during the MOBIUS ANT web seminar, virtually held in Montreal (8 April 2021).
• I gave a talk on my paper about "random multiplicative functions" during the Vibrant conference, virtually held in Brazil (18 March 2021). Here is the video: https://www.youtube.com/watch?v=ggvXbpP0VQg&ab_channel=AnalyticandProbabilisticNumberTheorySeminar.
• I gave a talk on ''Maximal random product sets'' during the "NT online conference", virtually held in Turin (18 February 2021). Here is the video: https://www.numbertheoryonline.org/recordings/.
• Contributed speaker at the "IML Number Theory seminar", virtually held in Stochkolm (8 February 2021).
• I gave a talk about ''A new elementary proof of the Prime Number Theorem'' (University of Warwick, 11 March 2020).
• I took part, giving also some talks, in the study group about "The Duffin&Schaeffer conjecture", held in the University of Warwick.
• Contributed speaker at the WIMP conference, held in the University of Warwick.
• Contributed speaker at the Warwick Y-RANT conference.
• Invited speaker at the 4th Number Theory Meeting Torino.
• I gave a talk on the occasion of the "Speaking with Style" conference, held in the University of Warwick.
• I took part, giving also some talks, in the study group about "Low moments of random multiplicative functions", held in the University of Warwick.
• I started the Mathematical blog A Sequence of IID Random PostsLink opens in a new window together with Peter MühlbacherLink opens in a new window.
• I gave a talk about ''Heuristics for the distribution of primes in short intervals'' (University of Warwick, 23 January 2019).
• I take part in the activities of the Number Theory group at Warwick. During the terms there is a running SeminarLink opens in a new window as well as a Study group.
• I attended several talks in the context of the Combinatorics Seminar, Probability Seminar and Colloquium.
• I gave a talk on the occasion of The fifth mini symposium of the Roman Number Theory AssociationLink opens in a new window about my paper Positive proportion of short intervals containing a prescribed number of primesLink opens in a new window.

Conferences Attended and Scheduled:

• SSANT Paris 2021Link opens in a new window (28 June-02 July 2021).
• MOBIUS ANT mini course, by Asif Zaman (May 2021).
• Number Theory OnlineLink opens in a new window (18/02/2021, 24/02/2021, 4/03/2021, Turin).
• Research program in Number Theory at Mittag-Leffler InstituteLink opens in a new window (11/01/2021-26/03/2021, Stockholm; winner of a junior fellowship).
• Nancy Analytic and Probabilistic Number Theory DaysLink opens in a new window (June 2020, Nancy).
• The Duffin and Schaeffer conjectureLink opens in a new window (December 2019, Bristol).
• Zeta FunctionsLink opens in a new window (December 2019, at CIRM).
• Warwick-Imperial Autumn MeetingLink opens in a new window (November 2019).
• Young researchers in Algebraic and Analytic Number Theory conferenceLink opens in a new window (November 2019).
• 4th Number Theory Meeting TorinoLink opens in a new window (October 2019).
• Warwick-Oxbridge-Manchester-Bristol-London (WOMBL) 1-day meeting at OxfordLink opens in a new window (September 2019).
• Second Symposium on Analytic Number TheoryLink opens in a new window (July 2019).
• Mini-Symposium on "Additive Combinatorics" at the British Combinatorial ConferenceLink opens in a new window (July-August 2019).
• The fifth mini symposium of the Roman Number Theory AssociationLink opens in a new window (April 2019).
• Warwick-Oxbridge-Manchester-Bristol-London (WOMBL) 1-day meeting at CambridgeLink opens in a new window (January 2019).
• Warwick-Imperial Autumn MeetingLink opens in a new window (December 2018).
• The fourth mini symposium of the Roman Number Theory Association Link opens in a new window(April 2018).
• Giornate INDAM di Teoria dei NumeriLink opens in a new window (December 2017).

• The third mini symposium of the Roman Number Theory Association Link opens in a new window(April 2017).

Here is a link to a brief version of my CVLink opens in a new window, containing information on my previous educational background and awards received.

Here is my Bachelor thesis in Italian: ''The rationality of the Zeta function of algebraic varieties''.Link opens in a new window

Here is my Master thesis in Italian: ''On recent results about short gaps between consecutive primes''.Link opens in a new window