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We describe a method to show that certain elliptic surfaces do not admit purely inseparable multisections (equivalently, that genus 1 curves over function fields admit no points over the perfect closure of the base field) and use it to show that any non-Jacobian elliptic structure on a very general supersingular K3 surface has no purely inseparable multisections. We also describe specific examples of genus 1 fibrations on supersingular K3 surfaces without purely inseparable multisections.

We prove that a twisted Enriques (respectively, untwisted bielliptic) surface over an algebraically closed field of positive characteristic at least 3 (respectively, at least 5) has no non-trivial Fourier-Mukai partners.

OBJECTIVES: The primary objective of this study was to assess the relationship between heat exposure and occupational traumatic injuries among construction workers. METHODS: We assessed the relationship between humidex, a measure of apparent temperature, and Washington State Fund workers’ compensation injuries among outdoor construction workers using a case-crossover design with time-stratified referent selection. Warm month (March–October) adult outdoor construction traumatic injury claims from 2000–2012 were spatiotemporally joined with high-resolution meteorological data. We used conditional logistic regression with linear splines to assess the association between maximum daily humidex and injuries. RESULTS: There were 63 720 occupational traumatic injury claims in construction that met our eligibility criteria during the study period. The traumatic injury odds ratio (OR) was 1.005 [95% confidence interval (CI) 1.003–1.007] per one °C change in humidex. In the spline analyses, we observed a nearly linear association of humidex with the risk of a traumatic injury. Effect estimates were higher among younger (18–24 years) and older (>54 years) workers, workers with lower extremity injuries, workers with less job experience, smaller employers, workers working in Western Washington, and time of injury before 12:30 hours, although CI of effect estimates overlapped in stratified analysis categories. CONCLUSIONS: In this study of Washington outdoor construction workers, increasing maximum daily humidex was associated with increasing traumatic injury risk. Further work should explore mechanisms of the association between heat exposure and traumatic injuries. Injury prevention efforts targeted at construction should address heat-related risk factors. In addition, heat awareness campaigns should address outcomes beyond heat-related illness.

We prove that every Brauer class over a field splits over a torsor under an abelian variety. If the index of the class is not congruent to 2 modulo 4, we show that the Albanese variety of any smooth curve of positive genus that splits the class also splits the class, and there exist many such curves splitting the class. We show that this can be false when the index is congruent to 2 modulo 4, but adding a single genus 1 factor to the Albanese suffices to split the class., Comment: 11 pages, references and acknowledgments updated, comments welcome at any time

Objectives: The primary objective of this study was to assess the relationship between heat exposure and occupational injuries in construction workers.Methods: The relationship between maximum dail...

Computer vision has already impacted a diverse field of applications, ranging from industrial robotics, intelligent and autonomous vehicles, security surveillance, manufacturing inspection, and human-computer interaction. Furthermore, digital imaging technologies are advancing ever smaller in size, finer in granularity, and faster in processing, while becoming less expensive and thus more accessible to businesses, organizations, and individuals in devices such as smart phones and tablets. Consumer products such as the Kinect™ offer advanced marker-less 3D motion capture capabilities at a low cost. New computer vision methods are now being researched and developed for occupational ergonomics applications. It is anticipated that these new tools will profoundly impact the future of occupational ergonomics and provide a variety of new instruments and techniques for design, analysis and evaluation in the practice of ergonomics. A panel of leading experts will describe some of the cutting edge research they are pursuing utilizing computer vision for occupational ergonomics applications. Radwin, Lee and Li use algorithms that track pixel patterns recorded from conventional video for quantifying repetitive hand motion, manual lifting and whole-body activities. Lee and Li describe the use computer vision tools to predict joint angles for a whole-body link model. Lieblich and Park describe the use of Kinect™ for classifying postures and generating individualized task specific avatars. Each of these approaches has specific advantages and limitations, which will be addressed by the panel. A discussion will follow exploring future research needs as well as engaging in a discussion among panelists and attendees about the needs, limitations, and obstacles that this new technology faces in bringing it into practice.

We introduce a formalism of descent of moduli spaces, and use it to produce limit linear series moduli spaces for families of curves in which the components of fibers may have monodromy. We then construct a universal stack of limit linear series over the stack of semistable curves of compact type, and produce new results on existence of real curves with few real linear series., 23 pages, journal reference added

The standard period-index conjecture for the Brauer group of a field of transcendence degree 2 over a $p$-adic field predicts that the index divides the cube of the period. Using Gabber's theory of prime-to-$\ell$ alterations and the deformation theory of twisted sheaves, we prove that the index divides the fourth power of the period for every Brauer class whose period is prime to $6p$, giving the first uniform period-index bounds over such fields., Final version, to appear in Inventiones

In an earlier paper the notion of a filtered derived equivalence was introduced, and it was shown that if two K3 surfaces admit such an equivalence, then they are isomorphic. In this paper we study more refined aspects of filtered derived equivalences related to the action on the cohomological realizations of the Mukai motive. It is shown that if a filtered derived equivalence between K3 surfaces also preserves ample cones then one can find an isomorphism that induces the same map as the equivalence on the cohomological realizations.

We give a modern introduction to the moduli of sheaves. After reviewing the classical theory, we give a catalogue of results from the last decade. We then consider a more "symmetric" formulation of the theory by working with gerbes from the start., Comment: 26 pages, contribution to proceedings of 2015 AMS Summer Institute in Algebraic Geometry

We study multiview moduli problems that arise in computer vision. We show that these moduli spaces are always smooth and irreducible, in both the calibrated and uncalibrated cases, for any number of views. We also show that these moduli spaces always admit open immersions into Hilbert schemes for more than two views, extending and refining work of Aholt-Sturmfels-Thomas. We use these moduli spaces to study and extend the classical twisted pair covering of the essential variety., Comment: Shortened version, to appear in SIAGA. Note that theorem, etc., numbering is different in published version than it is here. Corrected notational error in Notation 3.2 and Proposition 3.3, enhanced reference capitalization

Background Recent research suggests that heat exposure may increase the risk of traumatic injuries. Published heat-related epidemiological studies have relied upon exposure data from individual weather stations. Objective To evaluate the association between heat exposure and traumatic injuries in outdoor agricultural workers exposed to ambient heat and internal heat generated by physical activity using modeled ambient exposure data. Methods A case-crossover study using time-stratified referent selection among 12,213 outdoor agricultural workers with new Washington State Fund workers’ compensation traumatic injury claims between 2000 and 2012 was conducted. Maximum daily Humidex exposures, derived from modeled meteorological data, were assigned to latitudes and longitudes of injury locations on injury and referent dates. Conditional logistic regression was used to estimate odds ratios of injury for a priori daily maximum Humidex categories. Results The mean of within-stratum (injury day and corresponding referent days) standard deviations of daily maximum Humidex was 4.8. The traumatic injury odds ratio was 1.14 (95% confidence interval 1.06, 1.22), 1.15 (95% confidence interval 1.06, 1.25), and 1.10 (95% confidence interval 1.01, 1.20) for daily maximum Humidex of 25–29, 30–33, and ≥34, respectively, compared to < 25, adjusted for self-reported duration of employment. Stronger associations were observed during cherry harvest duties in the June and July time period, compared to all duties over the entire study period. Conclusions Agricultural workers laboring in warm conditions are at risk for heat-related traumatic injuries. Combined heat-related illness and injury prevention efforts should be considered in high-risk populations exposed to warm ambient conditions in the setting of physical exertion.

We show that the number of deformation types of canonically polarized manifolds over an arbitrary variety with proper singular locus is nite, and that this number is uniformly bounded in any nite type family of base varieties. As a corollary we show that a direct generalization of the geometric version of Shafarevich’s original conjecture holds for innitesimally rigid families of canonically polarized varieties.

Given a proper morphism X → S X\to S , we show that a large class of objects in the derived category of X X naturally form an Artin stack locally of finite presentation over S S . This class includes S S -flat coherent sheaves and, more generally, contains the collection of all S S -flat objects which can appear in the heart of a reasonable sheaf of t t -structures on X X . In this sense, this is the Mother of all Moduli Spaces (of sheaves). The proof proceeds by studying the finite presentation properties, deformation theory, and Grothendieck existence theorem for objects in the derived category, and then applying Artin’s representability theorem.

The reporting of research in a manner that allows reproduction in subsequent investigations is important for scientific progress. Several details of the recent study by Patrizi et al, ‘Comparison between low-cost marker-less and high-end marker-based motion capture systems for the computer-aided assessment of working ergonomics,’ are absent from the published manuscript and make reproduction of findings impossible. As new and complex technologies with great promise for ergonomics develop, new but surmountable challenges for reporting investigations using these technologies in a reproducible manner arise.Practitioner summary:As with traditional methods, scientific reporting of new and complex ergonomics technologies should be performed in a manner that allows reproduction in subsequent investigations and supports scientific advancement.

Objectives: Existing methods for practically evaluating musculoskeletal exposures such as posture and repetition in workplace settings have limitations. We aimed to automate the estimation of parameters in the revised United States National Institute for Occupational Safety and Health (NIOSH) lifting equation, a standard manual observational tool used to evaluate back injury risk related to lifting in workplace settings, using depth camera (Microsoft Kinect) and skeleton algorithm technology. Methods: A large dataset (approximately 22,000 frames, derived from six subjects) of simultaneous lifting and other motions recorded in a laboratory setting using the Kinect (Microsoft Corporation, Redmond, Washington, United States) and a standard optical motion capture system (Qualysis, Qualysis Motion Capture Systems, Qualysis AB, Sweden) was assembled. Error-correction regression models were developed to improve the accuracy of NIOSH lifting equation parameters estimated from the Kinect skeleton. Kinect-Qualysis errors were modelled using gradient boosted regression trees with a Huber loss function. Models were trained on data from all but one subject and tested on the excluded subject. Finally, models were tested on three lifting trials performed by subjects not involved in the generation of the model-building dataset. Results: Error-correction appears to produce estimates for NIOSH lifting equation parameters that are more accurate than those derived from the Microsoft Kinect algorithm alone. Our error-correction models substantially decreased the variance of parameter errors. In general, the Kinect underestimated parameters, and modelling reduced this bias, particularly for more biased estimates. Use of the raw Kinect skeleton model tended to result in falsely high safe recommended weight limits of loads, whereas error-corrected models gave more conservative, protective estimates. Conclusions: Our results suggest that it may be possible to produce reasonable estimates of posture and temporal elements of tasks such as task frequency in an automated fashion, although these findings should be confirmed in a larger study. Further work is needed to incorporate force assessments and address workplace feasibility challenges. We anticipate that this approach could ultimately be used to perform large-scale musculoskeletal exposure assessment not only for research but also to provide real-time feedback to workers and employers during work method improvement activities and employee training.

We describe some recent work on the uses of twisted sheaves in algebra, arithmetic, and geometry. In particular, we touch on the role of twisted sheaves in: 1. The geometry of the period-index problem for the Brauer group 2. The connection between finiteness of the u-invariant and Colliot-Thelene’s conjecture on 0-cycles 3. The link between the Tate conjecture for K3 surfaces and finiteness of the set of isomorphism classes of K3 surfaces over a finite field 4. The geometry of rational curves on the moduli spaces of supersingular K3 surfaces

Given a finite field k of characteristic at least 5, we show that the Tate conjecture holds for K3 surfaces defined over the algebraic closure of k if and only if there are only finitely many K3 surfaces over each finite extension of k., Final version

We prove that, for a K3 surface in characteristic p > 2, the automorphism group acts on the nef cone with a rational polyhedral fundamental domain and on the nodal classes with finitely many orbits. As a consequence, for any non-negative integer g, there are only finitely many linear systems of irreducible curves on the surface of arithmetic genus g, up to the action of the automorphism group., 9 pages, comments welcome at any time. Correction to the statement of Theorem 2.1 and the authors' email addresses

We study moduli spaces of maximal orders in a ramified division algebra over the function field of a smooth projective surface. As in the case of moduli of stable commutative surfaces, we show that there is a Koll\'ar-type condition giving a better moduli problem with the same geometric points: the stack of blt Azumaya algebras. One virtue of this refined moduli problem is that it admits a compactification with a virtual fundamental class., Comment: 14 pages, comments still welcome!

We give an account of some recent work on the existence of rational points on varieties over function fields, starting with basic material on deformation theory and the bend-and-break theorem. We emphasize the connection with the geometry of moduli spaces and include a sketch of the irreducibility of M g as a model. All details are relegated to the references.

We prove the Nagata compactification theorem for any separated map of finite type between quasi-compact and quasi-separated algebraic spaces, generalizing earlier results of Raoult. Along the way we also prove (and use) absolute noetherian approximation for such algebraic spaces, generalizing earlier results in the case of schemes., 49 pages, various clarifications and bugfixes

We present a method for compactifying stacks of $\PGL_n$-torsors (Azumaya algebras) on algebraic spaces. In particular, when the ambient space is a smooth projective surface we use our methods to show that various moduli spaces are irreducible and carry natural virtual fundamental classes. We also prove a version of the Skolem-Noether theorem for certain algebra objects in the derived category, which allows us to give an explicit description of the boundary points in our compactified moduli problem., Comment: 28 pages. Major reogranization and clarification. Hypothesis removed; results as stated now apply to arbitrary stable bundles, with no constraint on the rank

We study stacks of slope-semistable twisted sheaves on orbisurfaces with projective coarse spaces and prove that in certain cases they have many of the asymptotic properties enjoyed by the moduli of slope-semistable sheaves on smooth projective surfaces., Comment: 27 pages; further clarification of the introduction; comments still welcome

We use twisted sheaves to study the problem of index reduction for Brauer classes. In general terms, this problem may be phrased as follows: given a field k, a k-variety X, and a class α ∈ Br(k), compute the index of the class α k(X) ∈ Br(X) obtained from α by extension of scalars to k(X). We give a general method for computing index reduction which refines classical results of Schofield and van den Bergh. When X is a curve of genus 1, we use Atiyah's theorem on the structure of stable vector bundles with integral slope to show that our formula simplifies dramatically, giving a complete solution to the index reduction problem in this case. Using the twisted Fourier-Mukai transform, we show that a similarly simple formula describes homogeneous index reduction on torsors under higher-dimensional abelian varieties.

If $C$ is a smooth curve over an algebraically closed field $k$ of characteristic $p$, then the structure of the maximal prime to $p$ quotient of the \'etale fundamental group is known by analytic methods. In this paper, we discuss the properties of the fundamental group that can be deduced by purely algebraic techniques. We describe a general reduction from an arbitrary curve to the projective line minus three points, and show what can be proven unconditionally about the maximal pro-nilpotent and pro-solvable quotients of the prime-to-$p$ fundamental group. Included is an appendix which treats the tame fundamental group from a stack-theoretic perspective., Comment: 26 pages. Significant revision; errors corrected, various points clarified

We consider the stack of coherent algebras with proper support, a moduli problem generalizing Alexeev and Knutson's stack of branchvarieties to the case of an Artin stack. The main results are proofs of the existence of Quot and Hom spaces in greater generality than is currently known and several applications to Alexeev and Knutson's original construction: a proof that the stack of branchvarieties is always algebraic, that limits of one-dimensional families always exist, and that the connected components of the stack of branchvarieties are proper over the base under certain hypotheses on the ambient stack., Comment: 9 pages; several sections and new results added; to appear in IMRN

We use twisted sheaves and their moduli spaces to study the Brauer group of a scheme. In particular, we (1) show how twisted methods can be efficiently used to re-prove the basic facts about the Brauer group and cohomological Brauer group (including Gabber's theorem that they coincide for a separated union of two affine schemes), (2) give a new proof of de Jong's period-index theorem for surfaces over algebraically closed fields, and (3) prove an analogous result for surfaces over finite fields. We also include a reduction of all period-index problems for Brauer groups of function fields over algebraically closed fields to characteristic 0, which (among other things) extends de Jong's result to include classes of period divisible by the characteristic of the base field. Finally, we use the theory developed here to give counterexamples to a standard type of local-to-global conjecture for geometrically rational varieties over the function field of the projective plane., Comment: 31 pages. Major changes to section 4.2.3; the "question" is now answered in the negative, with resulting applications to local-to-global problems. To appear in Compositio Mathematica

We study moduli of semistable twisted sheaves on smooth proper morphisms of algebraic spaces. In the case of a relative curve or surface, we prove results on the structure of these spaces. For curves, they are essentially isomorphic to spaces of semistable vector bundles. In the case of surfaces, we show (under a mild hypothesis on the twisting class) that the spaces are asympotically geometrically irreducible, normal, generically smooth, and l.c.i. over the base. We also develop general tools necessary for these results: the theory of associated points and purity of sheaves on Artin stacks, twisted Bogomolov inequalities, semistability and boundedness results, and basic results on twisted Quot-schemes on a surface., Comment: 65 pages, minor changes made and typographical errors corrected