# Programme Grant

New frameworks in metric Number

Theory: foundations and applications

 The Engineering and Physical Sciences Research Council (EPSRC) has awarded a £1.6 million Programme Grant (£2 million fEC) to Professors Sanju Velani and Victor Beresnevich at the Department of Mathematics of the University of York. Starting 1 June 2012 this six years award will fund a wide range of activities and appointments including 6 Research Assistantships, short and long term research visitors and an international workshop. * EPSRC is the main UK government agency for funding research and training in engineering and the physical sciences. "EPSRC Programme Grants are a flexible mechanism to provide funding to world-leading research groups to address significant major research challenges."
 The research programme aims to make significant contribution to fundamental problems in the theory of Diophantine approximation. While yielding spectacular achievements over centuries, the development of Diophantine approximation has crystallised some of today's major research challenges; in particular Littlewood's conjecture on multiplicative Diophantine approximation, the Duffin-Schaeffer conjecture on non-monotonic Diophantine approximation and the generalised Baker-Schmidt problem on Diophantine approximation on manifolds. These challenges form the backbone of our research programme. * Prior to York there were only 3 other programme grants across mathematical sciences awarded to run a research-led project, namely those held at Cambridge, Imperial and Oxford.
 Diophantine approximation continues to have important and exciting applications in other research disciplines and indeed real world problems. Definite and topical applications of Diophantine approximation are currently evolving in the rapidly developing area of electronic communication, which make use of the full power of recent advances in the theory of metric Diophantine approximation, in particular, work on the Khintchine-Groshev theory for manifolds in order to investigate the potential of multiple-input and multiple-output (MIMO) technologies. An inherent part of this programme will be to contribute to such applications and enhance any development process arising from the real world problems and involving ideas from number theory. * Diophantine approximation is a branch of number theory that can loosely be described as a quantitative analysis of the property that the rationals are dense in the real line. The theory dates back to the ancient Greeks and Chinese who discovered good rational approximations to $\pi$ in order to predict the position of planets and stars. Nowadays the theory is deeply intertwined with measure theory, ergodic theory, dynamical systems, fractal geometry and other areas of mathematics.

Career opportunities:

Over the period of the grant we will appoint al least six Post-Doctoral Research Assistants. If you have any enquiries regarding job opportinities, please get in touch.

Post-Doctoral Research Assisiants:

Dr. Pankaj Vishe (February 2013 -- September 2015). Left for a permanent Lectureship at Durham University

Dr. Felipe Ramirez (August 2013 -- June 2015) . Left for a permanent Assistant Professorship at Wesleyan University

Dr. Paloma Bengoechea  (September 2013 -- August 2016).  Left for a Post-Doc at ETH Zurich

Dr. Faustin Adiceam (June 2015 -- )

Dr. David Simmons (July 2015 -- )

Dr. Sam Chow (October 2016 -- )

Dr. Erez Nesharim  (October 2016 -- )

Prof. A. Tyrrell (Department of Electronics, York), Chair Prof. A. Burr (Department of Electronics, York)Prof. A.D. Pollington (National Science Foundation, Washington)Prof. J.A.G. Vickers (Department of Mathematics, Southampton)Prof. T. Wooley FRS (Department of Mathematics, Bristol)

In the news:

Visitors:

2016

Emmanuel Breuillard (Münster, Germany)  19 Sept. 2016 -- 23 Sept. 2016

Andy Pollington (NSF, USA):  2 July 2016 -- 24 July 2016

Bob Vaughan (Penn. State, USA): 20 June 2016 -- 12 July 2016

Anish Ghosh (TIFR):  14 March 2016  -- 1 April 2016

Simon Myerson (Oxford): 7 Feb 2016 -- 10 Feb 2016

2015

Mumtaz Hussain (University of Newcastle, Australia): 9 Nov 2015 -- 11 Dec 2015

Wofgang M. Schmidt (Boulder, USA): 14 July 2015 -- 18 July 2015

Andy Pollington (NSF, USA):  14 July 2015 -- 16 July 2015

Paul Voutier : 14 July 2015 -- 16 July 2015

Xiannan Li (Oxford): 9 Feb 2015 -- 11 Feb 2015

Bob Vaughan (Penn. State, USA): 14 June 2015 -- 20 June 2015

Martin Widmer (Royal Holloway): 27 May 2015 -- 29 May 2015

Francoise Dal'Bo-Milonet (Université Rennes 1): 14 Apr -- 23 Apr 2015

Vasili Bernik (Minsk): 26 Mar 2015 -- 3 May 2015

2014

Arnaud Durand (Université Paris-Sud, France): 29 Nov 2014 -- 6 Dec 2014

Oscar Marmon (University of Gottingen): 24 Nov 2014 -- 26 Nov 2014

Efthymios Sofos (University of Bristol): 17 Nov 2014 -- 22 Nov 2014

Jonathan Bober (University of Bristol):  10 Nov 2014 -- 12 Nov 2014

Paul Voutier: 3 Nov 2014 -- 5 Nov 2014

Freddie Manners (Oxford): 27 Oct 2014 -- 29 Oct 2014

Mumtaz Hussain (University of Newcastle, Australia): 22 Sep 2014 -- 16 Oct 2014

Jinpeng An (Peking University, China):  25 -- 27 June 2014

Anish Ghosh (TATA Institute, India): 25 June 2014

Jayadev Athreya (University of Illinois, USA): 25 June 2014

Alexander Gorodnik (University of Bristol, UK): 25 June 2014

Grigory Margulis (Yale, USA): 22 -- 30 June 2014

Andy Pollington (NSF, USA):  17 May 2014 -- 29 May 2014

Martin Widmer (Royal Holloway, London): 5 May 2014-- 9 May 2014

Vasili Bernik (Minsk, Belarus): 7 March 2014 -- 3 April 2014

Bob Vaughan (Penn State, USA): 4 March 2014 -- 8 March 2014

Faustin Adiceam (NUI, Maynooth, Ireland): 3 Feb 2014 -- 15 Feb 2014

2013

Oscar Marmon (University of Gottingen): 18 Nov 2013 -- 21 Nov 2013

Shanta Laishram (Indian Statistical Institute): 18 Sep 2013 -- 21 Sep 2013

Andy Pollington (NSF, USA):  3 Sep 2013 -- 23 Sep 2013

Alan Haynes (Bristol, UK) 21 May 2013 -- 24 May 2013

Natalia Budarina (NUI, Maynooth, Ireland) 25 April 2013 -- 28 April 2013

Vasili Bernik (Minsk, Belarus): 10 April 2013 -- 26 May 2013

Bob Vaughan (Penn State, USA): 2 March 2013 -- 7 March 2013

Faustin Adiceam (NUI, Maynooth, Ireland): 25 Feb 2013 -- 2 Mar 2013

Yuri Nesterenko (Moscow State University, Russia):  20 Feb 2013 -- 19 Mar 2013

Michael Kelly (University of Texas, Austin, USA): 1 Feb 2013 -- 7 Feb 2013

2012

Andy Pollington (NSF, USA):  10 Sep 2012 -- 21 Sep 2012

Jinpeng An (Peking University, China):  18 June 2012 -- 19 July 2012

Meetings:

York-BT Mathematics of MIMO

When: 14 June 2013 10:00-15:30.

Organisers:  K. Briggs (BT) and S. Velani (York)

Programme:

Morning Session

Introduction to the theory of MIMO by Prof. Alister Burr  (Department of Electronics, York)

Introduction to the practice of MIMO by Dr Micheal Fitch (BT Labs)

Afternoon Session

Diophantine approximation and MIMO by Evgeniy Zorin  (Department of Mathematics, York)

Open discussion on research directions and applicaions

Workshop on interactions between number theory and wireless communication: York2014

When: 19-23 May 2014

Where: University of York

Organisers:  V. Beresnevich, J. Levesley, S. Velani and E. Zorin (York)

Programme: see workshop website

Workshop on interactions between number theory and wireless communication: York2016

When: 4-8 July 2016

Where: University of York

Organisers:  V. Beresnevich (York), A. Burr (York), B. Nazer (Boston), S. Velani (York)

Programme: see workshop website