R. Alfaro, C. Alvarez, A. Andrés, E. Anita-Rangel, M. Araya, J. C. Arteaga-Velázquez, D. Avila Rojas, H. A. Ayala Solares, R. Babu, P. Bangale, E. Belmont-Moreno, A. Bernal, K. S. Caballero-Mora, T. Capistrán, A. Carramiñana, S. Casanova, U. Cotti, J. Cotzomi, S. Coutiño de León, E. De la Fuente, C. de León, P. Desiati, N. Di Lalla, R. Diaz Hernandez, M. A. DuVernois, J. C. Díaz-Vélez, K. Engel, T. Ergin, C. Espinoza, K. Fang, N. Fraija, S. Fraija, A. Galván-Gámez, J. A. García-González, F. Garfias, N. Ghosh, M. M. González, J. A. González, J. A. Goodman, S. Groetsch, D. Guevel, J. Gyeong, J. P. Harding, S. Hernández-Cadena, I. Herzog, J. Hinton, D. Huang, F. Hueyotl-Zahuantitla, P. Hüntemeyer, A. Iriarte, S. Kaufmann, A. Lara, K. Leavitt, J. Lee, T. Lewis, H. León Vargas, J. T. Linnemann, A. L. Longinotti, G. Luis-Raya, K. Malone, M. Martin, O. Martinez, J. Martínez-Castro, J. A. Matthews, P. Miranda-Romagnoli, P. E. Mirón-Enriquez, J. A. Morales-Soto, E. Moreno, M. Mostafá, M. Najafi, A. Nayerhoda, L. Nellen, N. Omodei, M. Osorio-Archila, E. Ponce, Y. Pérez Araujo, E. G. Pérez-Pérez, C. D. Rho, A. Rodriguez Parra, D. Rosa-González, M. Roth, H. Salazar, D. Salazar-Gallegos, A. Sandoval, M. Schneider, J. Serna-Franco, M. Shin, A. J. Smith, Y. Son, R. W. Springer, O. Tibolla, K. Tollefson, I. Torres, R. Torres-Escobedo, E. Varela, L. Villaseñor, X. Wang, Z. Wang, I. J. Watson, H. Wu, S. Yu, S. Yun-Cárcamo, X. Zhang, H. Zhou

The last five years have shown us that ultra-high-energy (UHE; $>$100 TeV) gamma-ray sources are ubiquitous, but the nature of these sources remain highly uncertain. UHE gamma rays can be produced via either leptonic (Inverse compton) or hadronic (pion decay) emission mechanisms. To decisively determine the emission mechanisms, multimessenger searches are essential. Neutrinos are of particular interest as they are only created via hadronic channels. In this work, we describe a metric to select high-quality UHE events from the High Altitude Water Cherenkov (HAWC) Observatory. We use this metric to search for correlations between HAWC archival data and IceCube public neutrino alerts. 24 spatial coincidences are found, which is higher than the number of events expected by random chance. Therefore, we conclude that there are likely associations between HAWC gamma rays and IceCube neutrinos, but the angular resolutions of the two instruments prevent us from conclusively making any definitive associations between the coincidences and specific astrophysical sources. More sensitive detectors are needed.