# Seminars this semester

May 22 | Mon | Barbara Bolognese (Sheffield) | Algebraic Geometry Learning Seminar |

02:00 | J11 | Categorical resolutions of singularities | |

May 23 | Tue | Haluk Sengun (Sheffield) | Number Theory Learning Seminar |

13:00 |
J-11 | Adelic story. Part III. | |

Abstract:Tensor product theorem, odds and ends. |
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May 23 | Tue | Sven Meinhardt (Sheffield) | Operator K-theory and Noncommutative Geometry Seminar |

14:00 | J11 | Group actions, group C*-algebra, crossed product algebras. | |

May 23 | Tue |
Magdalena Kedziorek (Lausanne) | Topology seminar |

16:00 | J11 | Rational commutative ring G-spectra | |

Abstract:Recently, there has been some new understanding of various possible commutative ring G-spectra. In this talk I will recall these possibilities and discuss the most naive (or trivial) commutative ring G-spectra. Then I will sketch the main ingredients coming into the proof that if G is finite and we work rationally these objects correspond to (the usual) commutative differential algebras in the algebraic model for rational G-spectra. This is joint work with David Barnes and John Greenlees. |
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May 24 | Wed | Kasia Rejzner (University of York) | Pure Maths Colloquium |

14:00 | J11 | Mathematical quantum field theory: from analysis to homological algebra | |

Abstract:In this talk I will give an overview of mathematical structures used in modern quantum filed theory. I will focus on notions from functional analysis, like nets of operator algebras, and show how these combine with homological algebra methods to provide a rigorous description of perturbative gauge theories on curved spacetimes and of effective quantum gravity. The framework I present is called perturbative algebraic quantum field theory (pAQFT) and it is an emerging new way of approaching mathematical foundations of QFT. |
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May 24 | Wed | Alvar Daza (Universidad Rey Juan Carlos) | Applied Mathematics Colloquium |

14:00 | Hicks, LT 10 |
Fractal basins and unpredictability in dynamical systems | |

Abstract:Basins of attraction take its name from hydrology, and in dynamical systems they refer to the set of initial conditions that lead to a particular final state. When different final states are possible, the predictability of the system depends on the structure of these basins. In this talk, we will revise the main kinds of fractal basin boundaries appearing in dissipative and Hamiltonian systems. Finally, we will introduce the concept of basin entropy in order to answer an apparently naïve question: how can we say that one basin is more unpredictable than another? |
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May 25 | Thu |
Anthony Licata (Canberra) | Algebra / Algebraic Geometry seminar |

16:00 | J11 | Hilbert schemes, Heisenberg algebras, and braid group actions | |

Abstract:Let X be the minimal resolution of an ADE simple singularity. The derived category of the Hilbert scheme of points on X is acted on by a number of interesting algebraic objects. For example, there is a`categorical Heisenberg action' on \oplus_n D(Hilb_n(X)), which categorifies the Nakajima-Grojnowski action on cohomology; in addition, there is also a braid group action on each D(Hilb_n(X)). The goal of the talk will be to explain how the categorical Heisenberg action gives rise to the categorical braid group action. Time permitting, we'll discuss the connection to Khovanov homology, and state some conjectures. |
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Jun 1 | Thu |
TBA | Algebra / Algebraic Geometry seminar |

16:00 | J11 | ||

Jun 6 | Tue |
Titanic Ten | Topology seminar |

16:00 | J11 | Gong Show | |

Abstract:Tea then ten ten-minute talks. |
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Jun 7 | Wed |
Haluk Sengun (Sheffield) | Operator K-theory and Noncommutative Geometry Seminar |

14:00 | J11 | The Baum-Connes conjecture. | |

Abstract:We make a gentle introduction to the Baum-Connes conjecture. |
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Jun 8 | Thu |
David Spencer (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | Introduction to elliptic curves Part 2 | |

Jun 8 | Thu |
Ciaran Meachan (Glasgow) | Algebra / Algebraic Geometry seminar |

16:00 | J11 | Universal functors and derived autoequivalences | |

Abstract:The group of autoequivalences of the derived category of coherent sheaves on a variety is an interesting and subtle geometric geometric object. Any autoequivalences beyond the 'standard' ones -- automorphisms of the variety itself, twists by line bundles, and homological shift -- should be thought of as 'hidden symmetries' of the variety. I will discuss new examples of such symmetries when the underlying variety is the Hilbert scheme of points on an Abelian surface. This is based on joint work with Andreas Krug. |
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Jun 9 | Fri |
Nikos Diamantis (Nottingham) | Number Theory seminar |

11:00 |
J11 |
Cohomology associated to general weight modular forms | |

Abstract:The cohomological interpretation of classical modular forms, of integral weight, has proved very fruitful for arithmetic applications. Bruggeman, Lewis and Zagier provided an analogous interpretation for Maass cusp forms. We will discuss joint work with Bruggeman and Choie that incorporates general real weight holomorphic modular forms into a similar cohomological framework as that of the Maass cusp forms. |
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Jun 9 | Fri | Marianna Korsos (Sheffield) | SP2RC seminar |

13:00 | LT 10 | On the evolution of pre-flare patterns in 3-dimensional real and simulated Active Regions | |

Abstract:In this presentation, we address newly discovered pre-flare behavioural patterns in typical sunspot groups by focusing on their evolution as a function of height above the solar surface in a 3-dimensional solar AR. Here, we further probe and apply the concept of the pre-flare behavioural patterns using a magneto-hydrodynamic (MHD) simulation generating solar-like flares. We introduce and discuss the relevant properties and the capability of pre-flare tracking of ARs to improve Space Weather forecasting by focusing on the evolution from the photosphere towards the chromosphere, Transition Region and low corona. The basis of a proxy measure of our approach is the so-called weighted horizontal gradient of magnetic field (W_GM) defined between spots of opposite polarities closer to the polarity inversion line(s) of an AR. The value and the temporal variation of W_GM is found to possess novel and potentially important diagnostic information about (i) the intensity of expected flares and (ii) the accuracy of onset time prediction. Next, we will demonstrate how, by tracking the temporal evolution of W_GM, distance between opposite polarity spots and the associated net flux at various heights in the lower solar atmosphere evolves as function of height. We show that this latter temporal behaviour across the chromosphere-low corona has fundamentally new forecast capabilities. We found, that at a certain height the converging of opposite polarities begins much earlier than at the photosphere or at other heights. Therefore we present a tool to identify the optimum height in the solar atmosphere for flare forecasting that may considerably increase the capability of the time prediction . |
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Jun 13 | Tue | Ariel Weiss (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | Elliptic curves over finite fields | |

Jun 15 | Thu |
Di Zhang (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | Elliptic curves over local fields | |

Jun 15 | Thu | Dr Catie Lichten (RAND corporation) | |

15:00 | LT C | Ever wondered what happens in a Think Tank and how these organisations influence Government policy? (https://www.eventbrite.co.uk/o/science-in-policy-7880796098) | |

Jun 15 | Thu |
Agnieszka Bodzenta (Edinburgh) | Algebra / Algebraic Geometry seminar |

16:00 | J11 | Tilting relative generators for birational morphisms | |

Abstract:For a birational morphism of smooth varieties f: X \to Y with the dimension of fibers bounded by one, the derived category of X admits a relative tilting object over Y. It is a direct sum of copies of the canonical line bundle restricted to relative canonical divisors of partial contractions g:X \to Z. It endows the derived category of X with a t-structure related to the map f. I will show that Y is the fine moduli space of simple quotients of O_X in the heart of this t-structure. I will also prove that the t-structures for f and any partial contraction g are related by two tilts in torsion pairs. This is a joint work with A. Bondal. |
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Jun 20 | Tue | Angelo Rendina (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | Elliptic curves over global fields: the weak Mordell-Weil theorem | |

Jun 22 | Thu |
Benjamin Schmidt (Austin, Texas) | Algebra / Algebraic Geometry seminar |

16:00 | J11 | The genus of space curves | |

Abstract:A 19th century problem in algebraic geometry is to understand the relation between the genus and the degree of a curve in complex projective space. This is easy in the case of the projective plane, but becomes quite involved already in the case of three dimensional projective space. In this talk I will give an introduction to the topic, introduce stability conditions in the derived category, and explain how the two can be related. This is based on joint work in progress with Emanuele Macri. |
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Jun 23 | Fri | Dr Jane Pratt (University of Exeter) | SP2RC seminar |

13:00 | LT 11 |
Magnetic islands under the influence of heating and current | |

Abstract:Magnetic reconnection is a fundamental process in plasmas, complementary to the dynamo. In astrophysical contexts, magnetic reconnection can be observed on large scales. In a fusion plasma, the goal is not only to observe, but to manipulate the reconnection process and the magnetic islands that result. I will present a broad review of magnetic reconnection. In the context of my own research, I present a numerical study of the dynamics of magnetic islands that are formed by magnetic reconnection. I explore how heating and current influence a magnetic island's growth, and discuss implications for suppression and prevention of a tearing mode in a tokamak fusion reactor. |
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Jun 26 | Mon |
Rudolf Chow (Sheffield) | Number Theory Learning Seminar |

12:00 |
J-11 | Elliptic curves over global fields: the descent procedure and the Mordell-Weil theorem over Q | |

Jun 28 | Wed |
Luca Pol (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | Elliptic curves over global fields: key invariants of elliptic curves | |

Jun 29 | Thu |
Ciaran Schembri (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | Group and Galois cohomology | |

Jun 29 | Thu |
Daniel Labardini-Fragoso (UNAM, Mexico) | Algebra / Algebraic Geometry seminar |

16:00 | J11 | Species with potential from surfaces with orbifold points | |

Abstract:Felikson-Shapiro-Tumarkin have shown that surfaces with marked points and orbifold points of order 2 give rise to cluster algebras. They have done so by associating skew-symmetrizable matrices to the triangulations of such surfaces, and by showing that flips of triangulations are compatible with matrix mutations. In this talk I will sketch a construction of 'species with potential' that Jan Geuenich and myself have given for these triangulations in the hope of being able to produce a representation-theoretic approach to the corresponding skew-symmetrizable cluster algebras similar to the approach given by Derksen-Weyman-Zelevinsky for skew-symmetric cluster algebras via quiver representations. |
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Jul 3 | Mon |
Ariel Weiss (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | The Birch and Swinnerton-Dyer conjecture | |

Jul 4 | Tue | Neil Dummigan (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | The Bloch-Kato conjecture Part 1 | |

Jul 6 | Thu |
Neil Dummigan (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | The Bloch-Kato conjecture Part 2 | |

Jul 11 | Tue | Neil Dummigan (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | The Bloch-Kato conjecture Part 3 | |

Jul 13 | Thu |
Neil Dummigan (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | The Bloch-Kato conjecture Part 4 | |

Oct 18 | Wed |
Thomas Prince (Imperial) | Algebra / Algebraic Geometry seminar |

16:00 | J11 | ||