# Seminars this semester

May 21 | Mon |
Angelo Rendina (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | Geometric definition of modular forms | |

May 22 | Tue | Paolo Stellari (Universita' degli studi di Milano) | Algebra / Algebraic Geometry seminar |

14:00 | J11 | TBA | |

Abstract:TBA |
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May 22 | Tue | Joseph Fernandez (Liverpool John Moores) | Cosmology, Relativity and Gravitation |

16:00 |
J11, Hicks |
Tidal encounters of compact binaries with massive black holes as a source of gravitational waves | |

Abstract:Massive black holes (MBHs) are ubiquitous in galactic centres. The extreme potential due to these objects dominates the surrounding dynamics, giving rise to physics not possible in other regions. These regions are of particular interest for gravitational wave astronomy, as several dynamical processes which can give rise to black hole (BH) binary mergers have been postulated. We show that compact binaries can survive close encounters with the MBH without being disrupted, and that they tend to become hard and eccentric. Since the GW merger time of binaries is sensitive to the semi-major axis length and eccentricity, we find that this leads to a reduction of the merger time by several orders of magnitude in some cases. Therefore, tidal encounters of stellar mass BH binaries with a MBH at the centre of galaxies can provide a new formation channel of BH mergers. We use Monte Carlo simulations to evaluate the effective spin of the binaries after the encounter We also provide a description of a simple scenario to understand how this process could take place the a larger astrophysical context. |
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May 23 | Wed |
Ciaran Meachan (University of Glasgow) | Algebra / Algebraic Geometry seminar |

13:00 |
Hicks LT09 |
Derived equivalent Hilbert schemes of points on K3 surfaces which are not birational | |

Abstract:Starting with two non-birational derived equivalent K3 surfaces, one can ask whether their Hilbert schemes of points are birational. In this talk, we will show that in some cases they are but in most cases they are not. This is joint work with Giovanni Mongardi and Kota Yoshioka. |
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May 23 | Wed | Daniil Proskurin (Kiev Taras Shevchenko University) | Pure Maths Colloquium |

14:00 | J11 | $C^*$-algebras generated by quonic commutation relations and extensions of non-commutative tori | |

Abstract:We consider $C^*$-algebras $A_{q_i}\Theta$ generated by relations of the following form $$a_i^*a_i=1+q_i a_ia_i^* a_i^*a_j=e^{2\pi\theta_{ij}} a_ja_i^*, \quad i\ne j i, \quad j=1,\ldots,d $$ where $-1 \lt q_i \lt 1$, $\theta_{ij}=-\theta_{ji}$, $i\ne j$. We show that $A_{q_i}\Theta \simeq A_{0}\Theta$ is an extension of higher-dimensional non-commutative tori and study its properties. |
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May 23 | Wed |
Xiaolei Zhao (Northeastern University) | Algebra / Algebraic Geometry seminar |

15:00 |
Hicks LT09 |
Twisted cubics on cubic fourfolds and stability conditions | |

Abstract:It is a classical result of Beauville and Donagi that Fano varieties of lines on cubic fourfolds are hyper-Kahler. More recently, Lehn, Lehn, Sorger and van Straten constructed a hyper-Kahler eightfold out of twisted cubics on cubic fourfolds. In this talk, I will explain a new approach to these hyper-Kahler varieties via moduli of stable objects on the Kuznetsov components. Along the way, we will derive several properties of cubic fourfolds as consequences. This is based on a joint work with Chunyi Li and Laura Pertusi. |
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May 23 | Wed |
Chunyi Li (University of Warwick) | Algebra / Algebraic Geometry seminar |

16:15 |
Hicks LT09 |
Bogomolov type inequality for Fano varieties with Picard number 1 | |

Abstract:I will talk about some basic facts about slope stable sheaves and the Bogomolov inequality. New techniques from stability conditions will imply new stronger bounds on Chern characters of stable sheaves on some special varieties, including Fano varieties, quintic threefolds and etc. I will discuss the progress in this direction and some related open problems. |
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May 24 | Thu |
Adel Betina (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | The modular curve | |

May 29 | Tue | Scott Balchin (Sheffield) | Magnitude Homology |

13:00 | J11 | Mangitude homology and persistent homology?? | |

May 29 | Tue | Elisa Postinghel (University of Loughborough) | Algebra / Algebraic Geometry seminar |

14:00 | J11 | ||

May 29 | Tue | Jessie Durk (Queen Mary UL) | Cosmology, Relativity and Gravitation |

16:00 |
LT09, Hicks |
Black hole lattices as inhomogeneous cosmological models | |

Abstract:The standard model of cosmology, ΛCDM, is based on the assumption that the Universe can be described by the homogeneous and isotropic FLRW solution to the Einstein field equations. The need to test whether the large-scale expansion of space is that of FLRW, or is instead modified by the presence of inhomogeneities, has lead to this assumption being relaxed. An interesting subset of inhomogeneous cosmologies include those dubbed black hole lattices. These are exact, fully-relativistic treatments of universes with a discretised matter content. We generalise an existing family of these to include a cosmological constant, structure formation and electric charge. For each new generalisation, we find a common behaviour of tending towards FLRW-like as the number of masses is increased, and for the addition of structures, we investigate the effect of gravitational interaction energies between clustered masses. |
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May 30 | Wed | Nebojsa Pavic (Sheffield) | ShEAF: postgraduate pure maths seminar |

16:00 | J11 Hicks | Intersection theory in algebraic geometry: History and motivation. | |

Abstract:In this talk I'm going to motivate the notion of intersection theory in algebraic geometry by considering the example of Riemannian surfaces and only requiring a basic knowledge of complex analysis and a little bit of complex differential geometry. If time permits, I will give a rigorous definition of intersection groups, so called Chow groups, and relate them to the example. |
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May 31 | Thu | S. Shelyag (Northumbria University) | |

10:00 | LT 10 | Do photospheric non-magnetic bright points exist? | |

Abstract:Recent high-resolution simulations of non-magnetic solar photospheric convection suggest the presence of a separate class of small-scale photospheric brightenings, which coincide with intergranular vortex tubes. In contrast to well-known magnetic bright points, these brightenings are not related to magnetic fields. In our presentation, using high-resolution simulations with MURaM and detailed radiative diagnostics of the simulated models, I will analyse the physical characteristics of these brightenings and their observability with current and future instruments for solar observations. |
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May 31 | Thu |
Adel Betina (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | Modular curve- Part 2 | |

Jun 4 | Mon |
Ariel Weiss (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | Hasse invariant | |

Jun 5 | Tue | Algebra / Algebraic Geometry seminar | |

14:00 | J11 | ||

Jun 6 | Wed | Ciaran Schembri (Sheffield) | ShEAF: postgraduate pure maths seminar |

16:00 | J11 Hicks | Fuchsian group | |

Abstract:Fuchsian groups are discrete subgroups of the special projective linear group. They act as isometries on the hyperbolic plane and are studied because of their role in generating Riemann surfaces among other things. In this talk I will outline their geometric properties and if time permits will discuss how they relate to modern number theory. |
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Jun 7 | Thu |
Adel Betina (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | Introduction to rigid analytic geometry- Part (1) | |

Jun 11 | Mon |
Adel Betina (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | Introduction to rigid analytic geometry- Part (2) | |

Jun 12 | Tue | Algebra / Algebraic Geometry seminar | |

14:00 | J11 | ||

Jun 14 | Thu |
Adel Betina (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | Introduction to rigid analytic geometry- Part (3) | |

Jun 18 | Mon |
Adel Betina (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | The canonical subgroup | |

Jun 19 | Tue | Algebra / Algebraic Geometry seminar | |

14:00 | J11 | ||

Jun 21 | Thu |
Adel Betina (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | Classicality | |

Jun 25 | Mon |
Adel Betina (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | Classicality of overconvergent modular forms | |

Jun 26 | Tue | Algebra / Algebraic Geometry seminar | |

14:00 | J11 | ||

Jun 27 | Wed |
Ariel Weiss (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | Hida families (classical treatment) | |

Jun 28 | Thu |
Adel Betina (Sheffield) | Number Theory Learning Seminar |

14:00 | J-11 | Hida families (a la Pilloni) | |

Jul 3 | Tue |
K-Theory, Hecke Algebras and Representation Theory | |

16:00 |
Lecture Theatre C | ||

Jul 4 | Wed |
K-Theory, Hecke Algebras and Representation Theory | |

09:30 |
Lecture Theatre C | ||

Jul 4 | Wed |
K-Theory, Hecke Algebras and Representation Theory | |

11:00 |
Lecture Theatre C | ||

Jul 4 | Wed |
K-Theory, Hecke Algebras and Representation Theory | |

14:00 |
Lecture Theatre C | ||

Jul 4 | Wed |
K-Theory, Hecke Algebras and Representation Theory | |

15:30 |
Lecture Theatre C | ||

Jul 5 | Thu |
K-Theory, Hecke Algebras and Representation Theory | |

09:30 |
Lecture Theatre C | ||

Jul 5 | Thu |
K-Theory, Hecke Algebras and Representation Theory | |

11:00 |
Lecture Theatre C | ||

Jul 5 | Thu |
K-Theory, Hecke Algebras and Representation Theory | |

14:00 |
Lecture Theatre C | ||

Jul 5 | Thu |
K-Theory, Hecke Algebras and Representation Theory | |

15:30 |
Lecture Theatre C | ||

Jul 6 | Fri |
K-Theory, Hecke Algebras and Representation Theory | |

09:30 |
Lecture Theatre C | ||

Jul 6 | Fri |
K-Theory, Hecke Algebras and Representation Theory | |

11:00 |
Lecture Theatre C | ||

Jul 6 | Fri |
K-Theory, Hecke Algebras and Representation Theory | |

14:00 |
Lecture Theatre C | ||

Jul 6 | Fri |
K-Theory, Hecke Algebras and Representation Theory | |

15:30 |
Lecture Theatre C | ||