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 and Probabilistic Number Theory.

Publications:

• Positive proportion of short intervals containing a prescribed number of primes (Accepted for publication, Bulletin of Australian Mathematical Society).
• An Upper Bound for the Moments of a G.C.D. related to Lucas Sequences (Accepted for publication, 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 (In Press, 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 multiplicative functions in arithmetic progressions (main PhD project). I am trying to improve the current upper and lower bounds for the moments of the gcd of n and u(n), with u(n) being a Lucas sequence. I am trying to extend my previous work on short intervals with a given number of primes.

Teaching:

I have been TA for the modules:

• 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 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 will give a talk on the occasion of The fifth mini symposium of the Roman Number Theory Association on my paper Positive proportion of short intervals containing a prescribed number of primes.

Conferences Attended and Scheduled:

• 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.