Sarah Browne

University of Sheffield


Picture of Sarah Browne

I am a PhD student in the School of Mathematics and Statistics at the University of Sheffield, under the supervision of Paul Mitchener. My areas of study are functional analysis and topology, and in particular I am looking at E-theory, a bivariant functor from C*-algebras to abelian groups. I am forming a topological spectrum for E-theory to apply in differential geometry.

MAS436/MAS6340 Functional Analysis

Lecture notes for Semester 2

Lecture notes for Semester 2 with corrections

Problem booklet for Semester 2

Chapter 6 Solutions

Chapter 7 Solutions

Chapter 8 Solutions

Chapter 9 Solutions

Solutions for each chapter will appear in due course, as the semester. For autumn semester lecture notes see Paul Mitchener's page. Previous exam papers and solutions can also be found there.

Papers

A Bott periodicity proof for real graded C*-algebras. arXiv.

Seminars and Talks

Cuntz' proof of Bott periodicity, April 2017, Operator K-theory seminar, University of Sheffield

Establishing a topology on on certain morphisms of C*-algebras, March 2017, YFAW, University of Glasgow

A quasi-spectrum for asymptotic morphisms of graded C*-algebras, March 2017, SOAR, University of Glasgow.

The E-theory spectrum for C*-algebras, October 2016, Pure Maths Colloquium, University of Southampton

Complex graded E-theory, April 2016, YFAW, Queen's University Belfast

E-theory spectrum for complex graded C*-algebras, March 2016, University of Glasgow.

E-theory spectrum for complex graded C*-algebras, January 2016, Winter School, Universitaet Muenster.

E-theory spectrum, August 2015, YMC*A, University of Copenhagen.

An Introduction to E-theory, June 2015, YFAW, Imperial College London

An Introduction to E-theory, May 2015, PGR Seminar, University of Sheffield

Cuntz' proof of Bott periodicity, July 2014, KK-theory seminar, University of Sheffield

E-theory, June 2014, KK-theory Seminar, University of Sheffield

De Rham Cohomology, June 2014, PGR Seminar, University of Sheffield

Hilbert Modules, June 2014, KK-theory Seminar, University of Sheffield

Conferences/Meetings

Upcoming:

Scottish Operator Algebra Research Seminar (SOAR), 24 March - 25 March 2017, University of Glasgow

Young Functional Analysts' Workshop, 29 March - 31 March 2017 , University of Glasgow

Applications of operator algebras: order, disorder and symmetry 26 June - 30 June 2017, International Centre for Mathematical Sciences

Conferences I have attended:

Scottish Operator Algebra Research Seminar (SOAR), 2 December - 3 December 2016, University of Glasgow

GAP XIV, 8th August - 12th August 2016, University of Sheffield

Young Mathematicians in C*-algebras, 25th July - 29th July 2016, Universitaet Muenster

Groups, Dynamics, and Operator Algebras, 18th July - 22nd July 2016, Queen Mary University of London

Young Functional Analysts' Workshop, 6th April - 9th April 2016, Queen's University Belfast

Scottish Operator Algebra Research Seminar (SOAR), 16 March - 17 March 2016, University of Aberdeen

Winter School on Isomorphism Conjectures and Geometry of Groups, 25 January - 29 January 2016, Universitaet Muenster

Young Mathematicians in C*-algebras, 17th August - 21st August 2015, University of Copenhagen

Focus Programme on C*-algebras, Visited July 2015, Universitaet Muenster

Young Functional Analysts' Workshop, 10 June - 12 June 2015, Imperial College London

Oberwolfach Seminar: K-Theory for Group C*-Algebras and Semigroup C*-Algebras, 12 October - 18 October 2014, Mathematisches Forschungsinstitut Oberwolfach

Young Researchers in Mathematics 2014, 30 June - 3 July 2014, University of Warwick

Young Functional Analysts Workshop 2014, 23 April - 25 April 2014, Lancaster University

I attend the Transpennine Topology Triangle meetings whenever they occur in Sheffield

Teaching and Outreach work

Currently I am assisting in tutorials for MAS221 Analysis which I am also marking for. I am also doing a Q&A lecture style session for analysis.

Outreach work

I am currently involved in Maths Academy Interactive Lecture Series, and now after helping for one year I am an organiser. In 2013 I gave a joint talk on Infinity and in 2014 a individual talk on Topology and the Euler characteristic.

In June 2014 I gave 4 lectures on the Euler Characteristic to year 10 students who visited the university for the day.

I also give talks for open days now and again, these have centralised around coding in the past but I'm moving towards more topological talks.

Previously

I studied my MMath degree at the University of Sheffield, where I undertook a fourth year project supervised by David Applebaum on the topic of Fourier series on finite abelian groups.

Contact Details

Sarah Browne
Room H10a, Hicks Building
email: slbrowne1@sheffield.ac.uk



Last updated: 27 April 2017