No, a woman cannot reproduce without sperm in the typical human reproductive process requiring fertilization of an egg by sperm. However, a process called parthenogenesis allows some species' females to reproduce without sperm. This process involves an egg developing into an embryo without fertilization.
Parthenogenesis: A Closer Look
Parthenogenesis, as noted in several sources (https://umbc.edu/stories/virgin-births-from-parthenogenesis-how-females-from-some-species-can-reproduce-without-males/, https://www.sciencedirect.com/topics/veterinary-science-and-veterinary-medicine/parthenogenesis, https://en.wikipedia.org/wiki/Parthenogenesis), is a form of asexual reproduction where an egg develops into an embryo without fertilization by a sperm. For parthenogenesis to occur, several conditions must be met. Females must be able to create egg cells (oogenesis) without sperm stimulation (https://umbc.edu/stories/virgin-births-from-parthenogenesis-how-females-from-some-species-can-reproduce-without-males/). Then, the eggs must develop into early-stage embryos independently (https://umbc.edu/stories/virgin-births-from-parthenogenesis-how-females-from-some-species-can-reproduce-without-males/).
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Examples: Parthenogenesis has been observed in several animal species, including some sharks (https://ocean.si.edu/ocean-life/sharks-rays/parthenogenesis-when-female-sharks-reproduce-without-mate) and California condors (https://www.npr.org/2021/12/01/1060612410/no-sperm-no-problem).
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Human Reproduction: While recent research has made advancements in creating human embryos in a laboratory setting without sperm or eggs (https://www.bbc.com/news/health-66715669), these are not natural instances of parthenogenesis. Current scientific understanding does not allow for human reproduction through natural parthenogenesis. The potential for future technologies to enable human parthenogenesis remains speculative (https://www.earth.com/news/pregnancy-without-men-mice/).
Other Mechanisms
It's important to note that the question could be interpreted in other ways. For example, other mechanisms mentioned in (http://www.zo.utexas.edu/courses/thoc/virginbirth.html) like budding from somatic cells are not typical reproductive methods for humans.
