I am a first year PhD student under the supervision of Dr Adam Harper.

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

Office: B0.15.

Research Interests:

The distribution of prime numbers (small, bounded and large gaps between primes), Additive Number Theory (especially, Goldbach's type problems), Multiplicative Number Theory, the elementary approach in Analytic Number Theory (with an emphasis on the pretentious approach developed by Granville and Soundararajan), the distribution of arithmetical functions, Sieve Theory, Additive Combinatorics, Probabilistic Number Theory and Metric Number Theory (mainly, Diophantine approximation and metric Poissonian property of sequences).

Publications:

• A lower bound for the variance of generalized divisor functions in arithmetic progressions (Preprint).
• Positive proportion of short intervals containing a prescribed number of primes (Published, Bulletin of Australian Mathematical Society).
• An Upper Bound for the Moments of a G.C.D. related to Lucas Sequences (Published, Rocky Mountain Journal of Mathematics).
• On numbers n with polynomial image coprime with the n-th term of a linear recurrence (Published, Bulletin of the Australian Mathematical Society).
• Short intervals containing a prescribed number of primes (Published, Journal of Number Theory).
• Weighted Average Number of Prime m-tuples lying on an Admissible k-tuple of Linear Forms (Preprint, ArXiv version).

Current Research:

I am studying lower bounds for the variance of sequences in arithmetic progressions (main PhD project). The sequences I have been studying so far are those of multiplicative functions (among which a particular class of examples are the divisor functions and their generalizations and the characteristic functions of smooth integers), additive functions and functions with an additive structure.

I am working on random product sets, trying to understand necessary conditions to guarantee maximal size for a product of random sets and constructing an efficient random model for the product set of the sums of two squares.

Teaching:

I have been TA for the modules:

• MA257 Introduction to Number Theory (Second term 2019/2020).
• MA258 Mathematical Analysis III (First term 2019/2020).
• MA257 Introduction to Number Theory (Second term 2018/2019).
• MA258 Mathematical Analysis III (First term 2018/2019).

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

• MA244 Analysis 3 (First term 2018/2019).
• MA251 Algebra 1: Advanced Linear Algebra (First term 2018/2019).
• MA259 Multivariable Calculus (First term 2018/2019).

Activities:

• 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 Posts together with Peter Mühlbacher.
• 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 Seminar 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 Association about my paper Positive proportion of short intervals containing a prescribed number of primes.

Conferences Attended and Scheduled:

• Nancy Analytic and Probabilistic Number Theory Days (June 2020, Nancy).
• The Duffin and Schaeffer conjecture (December 2019, Bristol).
• Zeta Functions (December 2019, at CIRM).
• Warwick-Imperial Autumn Meeting (November 2019).
• Young researchers in Algebraic and Analytic Number Theory conference (November 2019).
• 4th Number Theory Meeting Torino (October 2019).
• Warwick-Oxbridge-Manchester-Bristol-London (WOMBL) 1-day meeting at Oxford (September 2019).
• Second Symposium on Analytic Number Theory (July 2019).
• Mini-Symposium on "Additive Combinatorics" at the British Combinatorial Conference (July-August 2019).
• The fifth mini symposium of the Roman Number Theory Association (April 2019).
• Warwick-Oxbridge-Manchester-Bristol-London (WOMBL) 1-day meeting at Cambridge (January 2019).
• Warwick-Imperial Autumn Meeting (December 2018).
• The fourth mini symposium of the Roman Number Theory Association (April 2018).
• Giornate INDAM di Teoria dei Numeri (December 2017).

• The third mini symposium of the Roman Number Theory Association (April 2017).

Here is a link to a brief version of my CV, containing information on my previous educational background and awards received.