School of Physical Sciences

Let G be a finite group and p a prime. Then there is a well-defined (at the level of characters) process of p-modular reduction for representations of G. It sometimes happens that two different ordinary irreducible characters can become the same when reduced modulo p, and it is interesting to determine exactly when this happens. For example, if G is the symmetric group, and two ordinary irreducibles are obtained from each other by tensoring with the sign representation, then their reductions modulo 2 will be the same.

In this talk we consider this problem for the double covers of the symmetric groups in characteristic 2; in fact, we solve the more general problem of when the 2-modular reductions of two characters are proportional to each other. I will give the result, and explain some of the techniques used to prove it.

• Speaker: Matthew Fayers, Queen Mary University of London
• Wednesday 31 January 2024, 16:30-17:30
• Venue: MR12.
• Series: Algebra and Representation Theory Seminar; organiser: Adam Jones.

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Short Version: I will explain why immersed stable minimal hypersurfaces in R5 are flat. This is joint work with Otis Chodosh, Chao Li, and Douglas Stryker.

Long Version: The stable Bernstein problem asks whether an immersed stable minimal hypersurface in Rn is necessarily flat. If true the result implies, for example, a priori curvature estimates for immersed stable minimal hypersurfaces in Riemannian n-manifolds.

An important special case of the result, known as the Bernstein problem, asks the same question except for minimal graphs over a hyperplane (such graphs are in fact locally area minimising). The Bernstein problem was resolved in full in the 1960’s by works of Fleming, De Giorgi, Almgren, Simons, Bombieri, and Giusti, in turn driving a lot of progress in the development of geometric measure theory. It was shown that such a minimal graph must be flat if it lies in R8 or lower, whilst counterexamples exist in R9 and higher. The stable Bernstein theorem has counterexamples in R8 and above for related reasons.

The stable Bernstein theorem in its full generality remained essentially open until recently. The works of Schoen—Simon—Yau (1975) and Bellettini (2023) establish the result up to R7 assuming the minimal hypersurface has Euclidean volume growth. The full R3 case was resolved independently by works of Fischer-Colbrie—Schoen, do Carmo—Peng, and Pogorelov, all around 1980. In 2021, Chodosh—Li proved the stable Bernstein theorem in R4, using techniques from non-negative scalar curvature. They later found another proof using techniques from uniformly positive scalar curvature utilising Gromov’s mu-bubbles, showing that the Euclidean volume growth assumption holds a priori.

In this talk, I will discuss recent work (joint with Otis Chodosh, Chao Li, and Douglas Stryker) resolving the stable Bernstein problem in R5. Our proof uses instead techniques from the study of uniformly positive bi-Ricci curvature. We show that a suitable conformal change of metric (the Gulliver—Lawson metric) has uniformly positive bi-Ricci curvature in a spectral sense. This allows us to construct (warped) mu-bubbles with uniformly positive Ricci curvature in a spectral sense, from which we can establish a Bishop volume-comparison theorem (which is a subtle adaptation of a technique from Bray; indeed, our proof seems to break down in any higher dimensional situation). These ingredients allow us to establish a priori Euclidean volume growth for the minimal hypersurface allowing us to prove the result.

• Speaker: Paul Minter (Clay Institute, Princeton, Cambridge)
• Friday 19 January 2024, 14:00-15:00
• Venue: MR15.
• Series: Partial Differential Equations seminar; organiser: Dr Greg Taujanskas.

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Small molecule inhibition of viral proteases has been a successful anti-viral therapeutic strategy in HIV and HCV . Structural insight on the SARS -CoV-2 main protease (Mpro) and previous small molecule experience with intravenous SARS -CoV-1 inhibitors gave a starting point for an oral Mpro inhibitor program in response to the COVID -19 outbreak. Designing and synthesizing molecules in a peptidomimetic chemotype, the team investigated a number of cysteine traps as reversibly covalent inhibitors, while looking to confer sufficient metabolic stability and permeability to attain oral bioavailability. Systematically challenging the need for hydrogen bond donors throughout the pharmacophore proved a successful strategy for enhancing permeability. This resulted in the discovery of PF-7321332, the first oral SARS -CoV-2 Mpro inhibitor to reach clinical development.1

PF-7321332 showed pan-human coronavirus activity with selectivity over human proteases. Phase 1 healthy volunteer studies will be described, with and without combination of low dose ritonavir as a pharmacokinetic enhancer. The preclinical work to identify PF-7321332 (now known as nirmatrelvir) and the resulting Ph1 study was the basis for a combined Ph2/3 study in high-risk patients. Nirmatrelvir/ritonavir went on to receive emergency use authorization for the treatment of high risk COVID -19 patients in the United States as PAXLOVID in December of 2021, just 17 months after nirmatrelvir was first synthesized and received full FDA approval in May 2023.

The ‘start to finish’ drug discovery story will be presented from a medicinal chemist’s point of view.

• Speaker: Dr Dafydd Owen - Pfizer
• Monday 22 January 2024, 16:00-17:00
• Venue: BMS Lecture Theatre, Department of Chemistry.
• Series: Synthetic Chemistry Research Interest Group; organiser: Chung Tu.

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Short Version: I will explain why immersed stable minimal hypersurfaces in \R5 are flat. This is joint work with Otis Chodosh, Chao Li, and Douglas Stryker.

Long Version: The stable Bernstein problem asks whether an immersed stable minimal hypersurface in \Rn is necessarily flat. If true the result implies, for example, a priori curvature estimates for immersed stable minimal hypersurfaces in Riemannian n-manifolds.

An important special case of the result, known as the Bernstein problem, asks the same question except for minimal graphs over a hyperplane (such graphs are in fact locally area minimising). The Bernstein problem was resolved in full in the 1960’s by works of Fleming, De Giorgi, Almgren, Simons, Bombieri, and Giusti, in turn driving a lot of progress in the development of geometric measure theory. It was shown that such a minimal graph must be flat if it lies in \R8 or lower, whilst counterexamples exist in \R9 and higher. The stable Bernstein theorem has counterexamples in \R8 and above for related reasons.

The stable Bernstein theorem in its full generality remained essentially open until recently. The works of Schoen—Simon—Yau (1975) and Bellettini (2023) establish the result up to \R7 assuming the minimal hypersurface has Euclidean volume growth. The full \R3 case was resolved independently by works of Fischer-Colbrie—Schoen, do Carmo—Peng, and Pogorelov, all around 1980. In 2021, Chodosh—Li proved the stable Bernstein theorem in \R4, using techniques from non-negative scalar curvature. They later found another proof using techniques from uniformly positive scalar curvature utilising Gromov’s mu-bubbles, showing that the Euclidean volume growth assumption holds a priori.

In this talk, I will discuss recent work (joint with Otis Chodosh, Chao Li, and Douglas Stryker) resolving the stable Bernstein problem in \R^5. Our proof uses instead techniques from the study of uniformly positive bi-Ricci curvature. We show that a suitable conformal change of metric (the Gulliver—Lawson metric) has uniformly positive bi-Ricci curvature in a spectral sense. This allows us to construct (warped) mu-bubbles with uniformly positive Ricci curvature in a spectral sense, from which we can establish a Bishop volume-comparison theorem (which is a subtle adaptation of a technique from Bray; indeed, our proof seems to break down in any higher dimensional situation). These ingredients allow us to establish a priori Euclidean volume growth for the minimal hypersurface allowing us to prove the result.

• Speaker: Paul Minter (Clay Institute, Princeton, Cambridge)
• Friday 19 January 2024, 14:00-15:00
• Venue: MR15.
• Series: Partial Differential Equations seminar; organiser: Dr Greg Taujanskas.

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A continuous flow of cells replenishes blood throughout life to maintain hematopoietic homeostasis. This flow originates from hematopoietic stem cells (HSCs) and progresses through a complex hierarchy of progenitors, collectively called hematopoietic stem and progenitor cells (HSPCs). The ever-increasing throughput of modern single cell ‘omics methods means that datasets encapsulating the cellular complexity of entire organ systems can now be generated. However, ‘omics protocols deliver snapshot measurements, because cells need to be destroyed to characterize their molecular states. As a result, it’s impossible to determine from those measurements how long it takes for a given cell to complete a differentiation process, nor at which precise stages cell numbers expand or contract.

New research from Göttgens group provides a strategy to create predictive dynamic models of a regenerative organ in vivo, at single cell resolution and over extended timeframes. The Göttgens team went on to use novel time-series datasets for blood development to generate new computational models capturing the tissue dynamics of mouse bone marrow haematopoiesis. This allowed the coupling of cascading single-cell expression patterns with dynamic changes in differentiation and growth speeds.

Changes in tissue dynamics underlie many major diseases, such as ageing associated defects in tissue maintenance and regeneration as well as clonal stem cell competition during early premalignant growth. To quantify such defects, researchers must first define tissue dynamics in the unperturbed healthy state. This new work provides such critical information for the blood system.

• Speaker: Bertie Gottgens, Cambridge Stem Cell Institute, University of Cambridge
• Thursday 25 January 2024, 16:00-17:00
• Venue: Biffen Lecture Theatre, Department of Genetics, Downing Site.
• Series: Computational and Systems Biology Seminar Series 2023 - 24; organiser: Aurora Gutierrez Antonio.

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The Breuil—Mézard conjecture concretely formulates the expectation that, under the Langlands correspondence, natural congruences between automorphic forms should be mirrored by congruences between Galois representations. In this talk I will explain some recent work which establishes new cases of this conjecture for crystalline representations of a ramified extension of Qp with small Hodge—Tate weights (roughly <= p/e). The approach is purely local and revolves around a comparison between moduli spaces of such representations and more explicit closed subschemes inside the affine grassmannian, constructed as degenerations of products of flag varieties. In particular, the methods also apply to moduli of Galois representations valued in more general split reductive groups than GLn.

• Speaker: Robin Bartlett (Glasgow)
• Tuesday 23 January 2024, 14:30-15:30
• Venue: MR13.
• Series: Number Theory Seminar; organiser: Hanneke Wiersema.

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The ice streams flowing into the Amundsen Sea, West Antarctica, are losing mass due to changes in the oceanic basal melting of their floating ice shelves. Rapid ice-shelf melting is sustained by the delivery of warm Circumpolar Deep Water to the ice-shelf cavities, which is first supplied to the continental shelf by an undercurrent that flows eastward along the shelf break. Temporal variability of this undercurrent controls variations in ice-shelf basal melt. Recent work shows that on decadal timescales the undercurrent variability opposes surface wind variability. Using a regional model, we show that this undercurrent variability is driven by sea-ice freshwater fluxes, particularly those north of the shelf break, which affect the cross-shelf break density gradient. This sea-ice variability is caused by tropical Pacific variability impacting atmospheric conditions over the Amundsen Sea. Ice-shelf melting also feeds back onto the undercurrent by affecting the on-shelf density and thereby influencing shelf-break density gradient anomalies.

• Speaker: Michael Haigh, British Antarctic Survey
• Wednesday 24 January 2024, 14:00-15:00
• Venue: BAS Seminar Room 1; zoom.
• Series: British Antarctic Survey - Polar Oceans seminar series; organiser: Dr Birgit Rogalla.

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This free event is open only to members of the University of Cambridge (and affiliated institutes). Please be aware that we are unable to offer consultations outside clinic hours.

If you would like to participate, please sign up as we will not be able to offer a consultation otherwise. Please sign up through the following link: https://forms.gle/fCU9SaGVq5u7wQnA9. Sign-up is possible from Mar 7 midday until Mar 11 midday or until we reach full capacity, whichever is earlier. If you successfully signed up, we will confirm your appointment by Mar 13 midday.

• Speaker: MR5 at the CMS
• Wednesday 13 March 2024, 16:30-18:00
• Venue: MR5.
• Series: Cambridge Statistics Clinic; organiser: Manuel Müller.

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This free event is open only to members of the University of Cambridge (and affiliated institutes). Please be aware that we are unable to offer consultations outside clinic hours.

If you would like to participate, please sign up as we will not be able to offer a consultation otherwise. Please sign up through the following link: https://forms.gle/mPMsKcFmSAVoMhT59. Sign-up is possible from Feb 22 midday until Feb 26 midday or until we reach full capacity, whichever is earlier. If you successfully signed up, we will confirm your appointment by Feb 28 midday.

• Speaker: MR5 at the CMS
• Wednesday 28 February 2024, 16:30-18:00
• Venue: MR5.
• Series: Cambridge Statistics Clinic; organiser: Manuel Müller.

Add to your calendar or Include in your list

This free event is open only to members of the University of Cambridge (and affiliated institutes). Please be aware that we are unable to offer consultations outside clinic hours.

If you would like to participate, please sign up as we will not be able to offer a consultation otherwise. Please sign up through the following link: https://forms.gle/Qmd2bef3cBHzMUwQ8. Sign-up is possible from Feb 8 midday until Feb 12 midday or until we reach full capacity, whichever is earlier. If you successfully signed up, we will confirm your appointment by Feb 14 midday.

• Speaker: MR5 at the CMS
• Wednesday 14 February 2024, 16:30-18:00
• Venue: MR5.
• Series: Cambridge Statistics Clinic; organiser: Manuel Müller.

Add to your calendar or Include in your list

This free event is open only to members of the University of Cambridge (and affiliated institutes). Please be aware that we are unable to offer consultations outside clinic hours.

If you would like to participate, please sign up as we will not be able to offer a consultation otherwise. Please sign up through the following link: https://forms.gle/6rQZ2JSNQ6Ehtc7X9. Sign-up is possible from Jan 25 midday until Jan 29 midday or until we reach full capacity, whichever is earlier. If you successfully signed up, we will confirm your appointment by Jan 31 midday.

• Speaker: MR5 at CMS
• Wednesday 31 January 2024, 16:30-18:00
• Venue: MR5.
• Series: Cambridge Statistics Clinic; organiser: Manuel Müller.

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Abstract not available

• Speaker: Tereza Jarníková, University of East Anglia
• Friday 09 February 2024, 13:00-14:00
• Venue: BAS Seminar Room 1; zoom.
• Series: British Antarctic Survey - Polar Oceans seminar series; organiser: Dr Birgit Rogalla.

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Experiments and numerical simulations have shown that turbulence in transitional wall-bounded shear flows such as plane Couette and Poiseuille flow frequently takes the form of long oblique bands, if the domains are sufficiently large to accommodate them. At their upper Reynolds-number threshold, laminar regions carve out gaps in otherwise uniform turbulence, thereby forming regular oblique turbulent-laminar patterns with a large spatial wavelength. At the lower threshold, isolated turbulent bands sparsely populate otherwise laminar domains and complete laminarization takes place via their disappearance characterized by the 2D directed percolation scenario.

• Speaker: Laurette Tuckerman, ESPCI Paris
• Friday 02 February 2024, 16:00-17:00
• Venue: MR2.
• Series: Fluid Mechanics (DAMTP); organiser: Professor Grae Worster.

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