Moduli Problems in Derived Noncommutative Geometry

We study moduli spaces of boundary conditions in 2D topological field theories. To a compactly generated linear infinity-category X, we associate a moduli functor M_X parametrizing compact objects in X. The Barr-Beck-Lurie monadicity theorem allows us to establish the descent properties of M_X, and show that M_X is a derived stack. The Artin-Lurie representability criterion makes manifest the relation between finiteness conditions on X, and the geometricity of M_X. If X is fully dualizable (smooth and proper), then M_X is geometric, recovering a result of Toën-Vaquie from a new perspective. Properness of X does not imply geometricity in general: perfect complexes with support is a counterexample. However, if X is proper and perfect (symmetric monoidal, with ``compact = dualizable\u27\u27), then M_X is geometric. The final chapter studies the moduli of Noncommutative Calabi-Yau Spaces (oriented 2D-topological field theories). The Cobordism Hypothesis and Deligne\u27s Conjecture are used to outline an approach to proving the unobstructedness of this space, and constructing a Frobenius structure on it

Reduction for SL(3)SL(3) pre-buildings

Given an $SL(3)$ spectral curve over a simply connected Riemann surface, we describe in detail the reduction steps necessary to construct the core of a pre-building with versal harmonic map whose differential is given by the spectral curve

Generators in formal deformations of categories

In this paper we use the theory of formal moduli problems developed by Lurie in order to study the space of formal deformations of a $k$-linear $\infty$-category for a field $k$. Our main result states that if $\mathcal{C}$ is a $k$-linear $\infty$-category which has a compact generator whose groups of self extensions vanish for sufficiently high positive degrees, then every formal deformation of $\mathcal{C}$ has zero curvature and moreover admits a compact generator.Comment: Preliminary version. Comments are welcome. 40

Constructing Buildings and Harmonic Maps

In a continuation of our previous work, we outline a theory which should lead to the construction of a universal pre-building and versal building with a $\phi$-harmonic map from a Riemann surface, in the case of two-dimensional buildings for the group $SL_3$. This will provide a generalization of the space of leaves of the foliation defined by a quadratic differential in the classical theory for $SL_2$. Our conjectural construction would determine the exponents for $SL_3$ WKB problems, and it can be put into practice on examples.Comment: 61 pages, 24 figures. Comments are welcom

Semistability, modular lattices, and iterated logarithms

We provide a complete description of the asymptotics of the gradient flow on the space of metrics on any semistable quiver representation. This involves a recursive construction of approximate solutions and the appearance of iterated logarithms and a limiting filtration of the representation. The filtration turns out to have an algebraic definition which makes sense in any finite length modular lattice. This is part of a larger project by the authors to study iterated logarithms in the asymptotics of gradient flows, both in finite and infinite dimensional settings.Comment: v2: new introduction, typos correcte

Modeling highly pathogenic avian influenza transmission in wild birds and poultry in West Bengal, India.

Wild birds are suspected to have played a role in highly pathogenic avian influenza (HPAI) H5N1 outbreaks in West Bengal. Cluster analysis showed that H5N1 was introduced in West Bengal at least 3 times between 2008 and 2010. We simulated the introduction of H5N1 by wild birds and their contact with poultry through a stochastic continuous-time mathematical model. Results showed that reducing contact between wild birds and domestic poultry, and increasing the culling rate of infected domestic poultry communities will reduce the probability of outbreaks. Poultry communities that shared habitat with wild birds or those indistricts with previous outbreaks were more likely to suffer an outbreak. These results indicate that wild birds can introduce HPAI to domestic poultry and that limiting their contact at shared habitats together with swift culling of infected domestic poultry can greatly reduce the likelihood of HPAI outbreaks

Predicting wildlife reservoirs and global vulnerability to zoonotic Flaviviruses.

Flaviviruses continue to cause globally relevant epidemics and have emerged or re-emerged in regions that were previously unaffected. Factors determining emergence of flaviviruses and continuing circulation in sylvatic cycles are incompletely understood. Here we identify potential sylvatic reservoirs of flaviviruses and characterize the macro-ecological traits common to known wildlife hosts to predict the risk of sylvatic flavivirus transmission among wildlife and identify regions that could be vulnerable to outbreaks. We evaluate variability in wildlife hosts for zoonotic flaviviruses and find that flaviviruses group together in distinct clusters with similar hosts. Models incorporating ecological and climatic variables as well as life history traits shared by flaviviruses predict new host species with similar host characteristics. The combination of vector distribution data with models for flavivirus hosts allows for prediction of  global vulnerability to flaviviruses and provides potential targets for disease surveillance in animals and humans

Global shifts in mammalian population trends reveal key predictors of virus spillover risk.

Emerging infectious diseases in humans are frequently caused by pathogens originating from animal hosts, and zoonotic disease outbreaks present a major challenge to global health. To investigate drivers of virus spillover, we evaluated the number of viruses mammalian species have shared with humans. We discovered that the number of zoonotic viruses detected in mammalian species scales positively with global species abundance, suggesting that virus transmission risk has been highest from animal species that have increased in abundance and even expanded their range by adapting to human-dominated landscapes. Domesticated species, primates and bats were identified as having more zoonotic viruses than other species. Among threatened wildlife species, those with population reductions owing to exploitation and loss of habitat shared more viruses with humans. Exploitation of wildlife through hunting and trade facilitates close contact between wildlife and humans, and our findings provide further evidence that exploitation, as well as anthropogenic activities that have caused losses in wildlife habitat quality, have increased opportunities for animal-human interactions and facilitated zoonotic disease transmission. Our study provides new evidence for assessing spillover risk from mammalian species and highlights convergent processes whereby the causes of wildlife population declines have facilitated the transmission of animal viruses to humans